Recent zbMATH articles in MSC 91Ahttps://zbmath.org/atom/cc/91A2024-04-15T15:10:58.286558ZWerkzeug\(k\)-color region select gamehttps://zbmath.org/1530.051252024-04-15T15:10:58.286558Z"Batal, Ahmet"https://zbmath.org/authors/?q=ai:batal.ahmet"Gügümcü, Neslihan"https://zbmath.org/authors/?q=ai:gugumcu.neslihanSummary: The region select game, introduced by Ayaka Shimizu, Akio Kawauchi and Kengo Kishimoto, is a game that is played on knot diagrams whose crossings are endowed with two colors. The game is based on the region crossing change moves that induce an unknotting operation on knot diagrams. We generalize the region select game to be played on a knot diagram endowed with \(k\)-colors at its vertices for \(2 \leq k \leq \infty \).Fugitive-search games on graphs and related parametershttps://zbmath.org/1530.051262024-04-15T15:10:58.286558Z"Dendris, Nick D."https://zbmath.org/authors/?q=ai:dendris.nick-d"Kirousis, Lefteris M."https://zbmath.org/authors/?q=ai:kirousis.lefteris-miltiades"Thilikos, Dimitris M."https://zbmath.org/authors/?q=ai:thilikos.dimitrios-mSummary: The goal of a fugitive-search game on a graph is to trap a fugitive that hides on the vertices of the graph by systematically placing searchers on the vertices. The fugitive is assumed to have complete knowledge of the graph and of the searchers' moves, but is restricted to move only along paths whose vertices are not guarded by searchers. The search number of the graph is the least number of searchers necessary to trap the fugitive. Variants of the fugitive-search game have been related to important graph parameters like treewidth and pathwidth. In this paper, we introduce a class of fugitive-search games where the searchers do not see the fugitive and the fugitive can only move just before a searcher is placed on the vertex it occupies. Letting the fugitive's speed (i.e. the maximum number of edges the fugitive can traverse at a single move) vary, we get different games. We show that if the speed of the fugitive is unbounded then the search number minus 1 is equal to the treewidth of the graph, while if the speed is 1 then the search number minus 1 is equal to the width, a polynomially computable graph parameter. We also show that in the above two cases, the search number remains the same even if we consider only these search strategies that at every step further restrict the fugitive's possible resorts (this monotonicity phenomenon is usually expressed as: ``recontamination does not help''). Finally, we show that for any graph, if the length of any chordless cycle is bounded by a constant \(s\) (\(s \geq 3\)), then the treewidth of the graph plus 1 is equal to the search number for fugitive speed \(s -2\).
For the entire collection see [Zbl 0813.68031].Hat guessing number for the class of planar graphs is at least 22https://zbmath.org/1530.051272024-04-15T15:10:58.286558Z"Latyshev, Aleksei"https://zbmath.org/authors/?q=ai:latyshev.aleksei"Kokhas, Konstantin"https://zbmath.org/authors/?q=ai:kokhas.konstantinSummary: We analyze the following version of the deterministic \textsc{Hats} game. We have a graph \(G\), and a sage resides at each vertex of \(G\). When the game starts, an adversary puts on the head of each sage a hat of a color arbitrarily chosen from a set of \(k\) possible colors. Each sage can see the hat colors of his neighbors but not his own hat color. All of the sages are asked to guess their own hat colors simultaneously, according to a predetermined guessing strategy and the hat colors they see, where no communication between them is allowed. The strategy is winning if it guarantees at least one correct individual guess for every color assignment. In a modified version of the hat guessing game each sage makes \(s \geqslant 1\) guesses. Given a graph \(G\) and integer \(s \geqslant 1\), the hat guessing number \(\operatorname{HG}_s(G)\) is the maximal number \(k\) such that there exists a winning strategy. In this paper, we present new constructors, i.e. theorems that allow built winning strategies for the sages on different graphs. Using this technique, we calculate the hat guessing number \(\operatorname{HG}_s(G)\) for paths and ``petunias'', and present a planar graph \(G\) for which \(\operatorname{HG}_1(G) \geq 22\).Slow coloring of \(3k\)-connected graphshttps://zbmath.org/1530.051282024-04-15T15:10:58.286558Z"Morris, Joan M."https://zbmath.org/authors/?q=ai:morris.joan-mSummary: The slow coloring game was introduced by \textit{T. Mahoney} et al. [Discrete Math. 341, No. 4, 1084--1093 (2018; Zbl 1380.05131)] and it is played by two players, Lister and Painter, on a graph \(G\). In round \(i\), Lister marks a nonempty subset \(M\) of \(V (G)\). By doing this he scores \(| M |\) points. Painter responds by deleting a maximal independent subset of \(M\). This process continues until all vertices are deleted. Lister aims to maximize the score, while Painter aims to minimize it. The best score that both players can guarantee is called the slow coloring number or sum-color cost of \(G\), denoted \(\mathring{\mathrm{s}} (G)\).
\textit{G. J. Puleo} and \textit{D. B. West} [Discrete Appl. Math. 262, 158--168 (2019; Zbl 1411.05184)] found that for an \(n\)-vertex tree \(T\), the slow coloring number is at most \(\lfloor \frac{3n}{2} \rfloor\), and that the maximum can be reached when \(T\) contains a spanning forest with vertices of degree 1 or 3. This implies that every \(n\)-vertex graph \(G\) having a perfect matching satisfies \(\mathring{\mathrm{s}} (G) \geq \lfloor \frac{3n}{2} \rfloor\). In this paper, we prove that for \(3k\)-connected graphs with \(|V(G)| \geq 4k\) and with a perfect matching the lower bound is higher: \(\mathring{\mathrm{s}} (G) \geq \frac{3n}{2} + k\).Balanced capacitieshttps://zbmath.org/1530.180102024-04-15T15:10:58.286558Z"Radul, Taras"https://zbmath.org/authors/?q=ai:radul.tarasThe Bondareva-Shapley Theorem [\textit{O. N. Bondareva}, Probl. Kibern. 10, 119--139 (1963; Zbl 1013.91501); \textit{L. S. Shapley}, Int. J. Game Theory 1, 11--26 (1971; Zbl 0222.90054)] provides a characterization of games on finite sets with non-empty core, claiming the the core is non-empty iff the game is balanced. This paper considers a cooperative game on a compactum. The author established in \S 2 an analogue of Bondareva-Shapley theorem that non-emptiness of the core is equivalent to balancedness of the game.
Capacities (non-additive measures, fuzzy measures) were introduced by \textit{G. Choquet} [Ann. Inst. Fourier 5, 131--295 (1955; Zbl 0064.35101)]. Capacities can be considered as monotone cooperative games. Capacities on compacta were considered in [\textit{L. Zhou}, Trans. Am. Math. Soc. 350, No. 5, 1811--1822 (1998; Zbl 0905.28006)], where the important role plays the upper-semicontinuity property connecting the capacity theory with the topological structure. The author gives a characterization of some fuzzy integrals generated by balanced capacities in \S 4.
Categorical and topological properties of spaces of upper-semicontinuous normed capacities on compact Hausdorff spaces (compacta) were investigated in [\textit{M. M. Zarichnyǐ} and \textit{O. R. Nykyforchyn}, Sb. Math. 199, No. 2, 159--184 (2008; Zbl 1165.54003); translation from Mat. Sb. 199, No. 2, 3--26 (2008)]. The author considers categorical properties of balanced capacities in \S 3.
Reviewer: Hirokazu Nishimura (Tsukuba)Regularity and long time behavior of one-dimensional first-order mean field games and the planning problemhttps://zbmath.org/1530.353172024-04-15T15:10:58.286558Z"Mimikos-Stamatopoulos, Nikiforos"https://zbmath.org/authors/?q=ai:mimikos-stamatopoulos.nikiforos"Munoz, Sebastian"https://zbmath.org/authors/?q=ai:munoz.sebastianSummary: We study the regularity and long time behavior of the one-dimensional, local, first-order mean field games system and the planning problem, assuming a Hamiltonian of superlinear growth, with a nonseparated, strictly monotone dependence on the density. We improve upon the existing literature by obtaining two regularity results. The first is the existence of classical solutions without the need to assume blow-up of the cost function near small densities. The second result is the interior smoothness of weak solutions without the need to assume either blow-up of the cost function or that the initial density be bounded away from zero. We also characterize the long time behavior of the solutions, proving that they satisfy the turnpike property with an exponential rate of convergence and identifying their limit as the solution of the infinite horizon system. Our approach relies on the elliptic structure of the system and displacement convexity estimates. In particular, we apply displacement convexity methods to obtain both global and local a priori lower bounds on the density.A continuous dependence estimate for viscous Hamilton-Jacobi equations on networks with applicationshttps://zbmath.org/1530.353332024-04-15T15:10:58.286558Z"Camilli, Fabio"https://zbmath.org/authors/?q=ai:camilli.fabio"Marchi, Claudio"https://zbmath.org/authors/?q=ai:marchi.claudioSummary: We study continuous dependence estimates for viscous Hamilton-Jacobi equations defined on a network \(\Gamma\). Given two Hamilton-Jacobi equations, we prove an estimate of the \(C^2\)-norm of the difference between the corresponding solutions in terms of the distance among the Hamiltonians. We also provide two applications of the previous estimate: the first one is an existence and uniqueness result for a quasi-stationary Mean Field Games defined on the network \(\Gamma\); the second one is an estimate of the rate of convergence for homogenization of Hamilton-Jacobi equations defined on a periodic network, when the size of the cells vanishes and the limit problem is defined in the whole Euclidean space.Stackelberg game approach to mixed stochastic \(H_2 /H_{\infty}\) control for mean-field jump-diffusions systemshttps://zbmath.org/1530.490302024-04-15T15:10:58.286558Z"Zhang, Suya"https://zbmath.org/authors/?q=ai:zhang.suya"Zhang, Weihai"https://zbmath.org/authors/?q=ai:zhang.weihai"Meng, Qingxin"https://zbmath.org/authors/?q=ai:meng.qingxinThe authors consider a filtered complete probability space \((\Omega , \mathcal{F},\mathbb{F},\mathbb{P})\), assuming that the filtration \(\mathbb{F} =\{F(r)\}_{0\leq r\leq T}\) satisfies the usual conditions of right continuity and \(\mathbb{P}\)-completeness, and the linear mean-field jump-diffusion system: \(dx(r)=[A(r)x(r-)+\overline{A}(r)\mathbb{E} [x(r-)]+B_{1}(r)u(r)+\overline{B}_{1}(r)\mathbb{E}[u(r)]+B_{2}(r)w(r)+ \overline{B}_{2}(r)\mathbb{E}[w(r)]dr+[C(r)x(r-)+\overline{C}(r)\mathbb{E} [x(r-)]+D_{1}(r)u(r)+\overline{D}_{1}(r)\mathbb{E}[u(r)]+D_{2}(r)w(r)+ \overline{D}_{2}(r)\mathbb{E}[w(r)]dW(r)+\int_{\mathbb{Z}}[E(\mathfrak{z} ,r)x(r-)+\overline{E}(\mathfrak{z},r)\mathbb{E}[x(r-)]+F_{1}(\mathfrak{z} ,r)u(r)+\overline{F}_{1}(\mathfrak{z},r)\mathbb{E}[u(r)]+F_{2}(\mathfrak{z} ,r)w(r)+\overline{F}_{2}(\mathfrak{z},r)\mathbb{E}[w(r)]]\widetilde{N}(d \mathfrak{z},dr)\), where \(x=x(t)\in \mathbb{R}^{n}\) is the state process, \( u(\cdot )\in \mathbb{R}^{m_{1}}\) the control input, \(w(\cdot )\in \mathbb{R} ^{m_{2}}\) the disturbance, \(z(\cdot )=\left( \begin{array}{c} Q(r)x(r) \\
R_{1}(r)u(r) \\
R_{2}(r)w(r) \end{array} \right) \in \mathbb{R}^{q}\) the output, \(A(\cdot ),\overline{A}(\cdot ),B_{i}(\cdot ),\overline{B}_{i}(\cdot ),C(\cdot ),\overline{C}(\cdot ),D_{i}(\cdot ),\overline{D}_{i}(\cdot ),E(\cdot ),\overline{E}(\cdot ),F_{i}(\)\textperiodcentered \(,\cdot ),\overline{F}_{i}(\cdot ,\cdot )\), \( i=1,2\), given deterministic matrix-valued functions with appropriate dimensions, \(\mathbb{E}\) the mathematical expectation, \(\{\widetilde{N}(d \mathfrak{z},dr)\}_{t\leq r\leq T}\) a Poisson random martingale measure, and \(W(\cdot )=\{W(r)\}_{t\leq r\leq T}\) a 1D standard Brownian motion. The authors decompose the mixed stochastic \(H_{2}/H_{\infty }\) control problem for the above system, first analyzing the \(H_{\infty }\) problem, considered as the follower problem. \(\mathbb{K}\) being a Hilbert space, they define the space \(\mathcal{S}_{\mathcal{F}}^{2}(t,T;\mathbb{K})\) as the space of all \( \mathbb{K}\)-valued \(\mathcal{F}_{r}\)-adapted càdlàg processes \( g(\cdot )\) satisfying \(\mathbb{E}[sup_{t\leq r\leq T}\left\Vert g(r)\right\Vert _{\mathbb{K}}^{2}]<\infty \), the space \(\mathcal{L}_{ \mathcal{F}}^{2}(t,T;\mathbb{K})\) of all \(\mathbb{K}\)-valued \(\mathcal{F}_{r} \)-adapted stochastic processes \(g(\cdot )\) satisfying \(\mathbb{E}[\left\Vert \int_{t}^{T}g(r)\right\Vert _{\mathbb{K}}^{2}dr]<\infty \), the space \( \mathcal{L}_{\mathcal{F},p}^{2}(t,T;\mathbb{K})\) of all \(\mathbb{K}\)-valued \( \mathcal{F}_{r}\)-predictable stochastic processes \(g(\cdot )\) satisfying \( \mathbb{E}[\left\Vert \int_{t}^{T}g(r)dr\right\Vert _{\mathbb{K} }^{2}]<\infty \), for \(g:[t,T]\times \Omega \rightarrow \mathbb{K}\), and \( \mathcal{U}_{i}=\mathcal{L}_{\mathcal{F},p}^{2}(t,T;\mathbb{R}^{m_{i}})\). They derive the coupled system of two Riccati differential equations and the mean-field backward stochastic differential equations using the four-step scheme. Assuming the existence of solutions to the coupled Riccati differential equations, they prove the existence of a solution to the mean-field backward stochastic differential equations in \(\mathcal{S}_{ \mathcal{F}}^{2}(t,T;\mathbb{R}^{n})\times \mathcal{L}_{\mathcal{F} ,p}^{2}(t,T;\mathbb{R}^{n})\times \mathcal{L}_{\mathcal{F}}^{\nu ,2}([t,T]\times \mathbb{Z};\mathbb{R}^{n})\), they derive an explicit feedback representation of the optimal control associated with the follower problem and an equivalent formulation of the cost function. The authors then analyze the \(H_{2}\) problem as the leader problem. They build the mean-field forward-backward stochastic differential equations. They prove that \(u^{\ast }(\cdot )\in \mathcal{U}_{1}\) is the optimal control for the \(H_{2}\) criterion if and only if the admissible control \(u^{\ast }(\cdot )\) satisfies some stationarity condition. Applying the convex variational method, they establish the mean-field stochastic maximum principle. Considering the two situations where the Poisson process \(N\) has a unit jump, or the control of follower does not appear in the part of the jump diffusion, they obtain the explicit feedback representation of the optimal control for the leader problem. They finally obtain a state-feedback representation for the open-loop Stackelberg equilibrium point. The paper ends with an example of a Principal-Agent problem involving moral hazard, where the profit process \(\mathcal{P}(r)\) is the solution to: \(d\mathcal{P} (r)=[\alpha (r)\mathcal{P}(r)+\beta _{1}(r)c(r)+\beta _{2}(r)a(r)]dr+[\lambda (r)\mathcal{P}(r)+\vartheta (r)c(r)+\varrho (r)a(r)]dW(r)+\int_{\mathbb{Z}}\mu (\mathfrak{z},r)\mathcal{P}(r)\widetilde{N }(d\mathfrak{z},dr)\), \(x(0)=0\), \(z(r)=[\frac{\rho }{2}Var[\mathcal{P} (r)]^{1/2}\), where \(z(\cdot )\) represents the standard deviation of the investment risk-return, \(\rho >0\) a constant weight, \(c(\cdot )\) the Principal-Agent contract designed by P for A, \(a(\cdot )\) A's investment strategy and behavioral strategy, \(\alpha (\cdot )\) the expected return of the portfolio, \(\beta _{1}(\cdot )\) P's selection parameter, \(\beta _{2}(\cdot )\) A's selection parameter, \(\lambda (\cdot )\) the portfolio volatility, \(\vartheta (\cdot )\) the contract's responsiveness to random changes over time, and \(\varrho (\cdot )\) A's strategy parameter. The authors here establish the corresponding optimal contract and optimal strategy.
Reviewer: Alain Brillard (Riedisheim)Optimal linear closed-loop Stackelberg strategy with asymmetric informationhttps://zbmath.org/1530.490312024-04-15T15:10:58.286558Z"Sun, Yue"https://zbmath.org/authors/?q=ai:sun.yue"Li, Hongdan"https://zbmath.org/authors/?q=ai:li.hongdan"Xu, Juanjuan"https://zbmath.org/authors/?q=ai:xu.juanjuan"Zhang, Huanshui"https://zbmath.org/authors/?q=ai:zhang.huanshuiSummary: In this paper, we consider the optimal linear closed-loop Stackelberg strategy for stochastic system where the state is unknown but observed though linear stochastic measurement systems. Particularly, the information structure is asymmetric where the leader can obtain the follower's measurement information and its historical control inputs, while the follower can only obtain its own measurement information and historical inputs, which have led to major challenge since the 1970s. It is well known that the closed-loop Stackelberg optimal control in general is a hard problem and no explicit solution can be derived. Instead, this paper aims to present a linear closed-loop solution to the problem. However, how to give a rational definition for the linear closed-loop Stackelberg controller is a difficulty. By using innovation, this paper defines the linear closed-loop Stackelberg controller with specified given gain matrices. Then the analytical solutions for the leader and the follower are given, respectively, which are the feedback form of the Kalman filtering and the optimal gain matrices for the leader and follower are obtained by decoupled solving two Riccati equations. Finally, by using the forward iteration algorithm, the coupled forward and backward Riccati equations are solved in infinite horizon, which overcomes the obstacles that the separation principle becomes invalid.Adversarial formal semantics of attack trees and related problemshttps://zbmath.org/1530.680502024-04-15T15:10:58.286558Z"Brihaye, Thomas"https://zbmath.org/authors/?q=ai:brihaye.thomas"Pinchinat, Sophie"https://zbmath.org/authors/?q=ai:pinchinat.sophie"Terefenko, Alexandre"https://zbmath.org/authors/?q=ai:terefenko.alexandreSummary: Security is a subject of increasing attention in our actual society in order to protect critical resources from information disclosure, theft or damage. The informal model of attack trees introduced by Schneier, and widespread in the industry, is advocated in the 2008 NATO report to govern the evaluation of the threat in risk analysis. Attack-defense trees have since been the subject of many theoretical works addressing different formal approaches.
In 2017, \textit{M. Audinot} et al. [Lect. Notes Comput. Sci. 10492, 83--102 (2017; Zbl 1496.68054)] introduced a path semantics over a transition system for attack trees. Inspired by the later, we propose a two-player interpretation of the attack-tree formalism. To do so, we replace transition systems by concurrent game arenas and our associated semantics consist of strategies. We then show that the emptiness problem, known to be NP-complete for the path semantics, is now \textsc{Pspace}-complete. Additionally, we show that the membership problem is \textsc{coNP}-complete for our two-player interpretation while it collapses to P in the path semantics.
For the entire collection see [Zbl 1522.68028].Deep reinforcement learning for \textsf{FlipIt} security gamehttps://zbmath.org/1530.680512024-04-15T15:10:58.286558Z"Greige, Laura"https://zbmath.org/authors/?q=ai:greige.laura"Chin, Peter"https://zbmath.org/authors/?q=ai:chin.peterFor the entire collection see [Zbl 1492.94005].Characterizing the decidability of finite state automata team games with communicationhttps://zbmath.org/1530.681432024-04-15T15:10:58.286558Z"Coulombe, Michael"https://zbmath.org/authors/?q=ai:coulombe.michael-j"Lynch, Jayson"https://zbmath.org/authors/?q=ai:lynch.jaysonSummary: In this paper we define a new model of limited communication for multiplayer team games of imperfect information. We prove that the Team DFA Game and Team Formula Game, which have bounded state, remain undecidable when players have a rate of communication which is less than the rate at which they make moves in the game. We also show that meeting this communication threshold causes these games to be decidable.
For the entire collection see [Zbl 1522.68028].Grounding game semantics in categorical algebrahttps://zbmath.org/1530.681542024-04-15T15:10:58.286558Z"Koenig, Jérémie"https://zbmath.org/authors/?q=ai:koenig.jeremieSummary: I present a formal connection between \textit{algebraic effects} and \textit{game semantics}, two important lines of work in programming languages semantics with applications in compositional software verification.
Specifically, the algebraic signature enumerating the possible side-effects of a computation can be read as a game, and strategies for this game constitute the free algebra for the signature in a category of complete partial orders (\textit{cpos}). Hence, strategies provide a convenient model of computations with uninterpreted side-effects. In particular, the operational flavor of game semantics carries over to the algebraic context, in the form of the coincidence between the initial algebras and the terminal coalgebras of cpo endofunctors.
Conversely, the algebraic point of view sheds new light on the strategy constructions underlying game semantics. Strategy models can be reformulated as ideal completions of partial strategy trees (free dcpos on the term algebra). Extending the framework to multi-sorted signatures would make this construction available for a large class of games.
For the entire collection see [Zbl 1522.68034].Adversarial strategy for transductive zero-shot learninghttps://zbmath.org/1530.682172024-04-15T15:10:58.286558Z"Liu, Youfa"https://zbmath.org/authors/?q=ai:liu.youfa"Du, Bo"https://zbmath.org/authors/?q=ai:du.bo"Ni, Fuchuan"https://zbmath.org/authors/?q=ai:ni.fuchuanSummary: Zero-shot learning (ZSL) realizes unseen object recognition by transferring knowledge from seen classes to unseen classes under common semantic space assumption, such as attribute space and semantic word vector space. Previous works used seen image feature and semantic representation but ignored unseen test image features to learn a projection from visual space to semantic space, which may lead to the domain shift problem, i.e., due to disjoint seen and unseen classes, the projection learnt from auxiliary dataset is biased when applied directly to the target dataset. In this paper, adversarial strategy is proposed with an instantiation to deal with domain shift problem. It is described as a two-player game in which player 1 is projector while player 2 is classifier. Projector expects to learn a projection from visual space to semantic space with good semantic preservation property while classifier expects to achieve high accuracy. The adversarial meaning comes from the design of parallel structure between loss function on training samples and that on test samples, semantic compatibility of these two loss functions and loss function in classifier, and distribution alignment. A theoretical analysis is provided and experiments are performed on benchmark datasets to ascertain the effectiveness of adversarial strategy.Controller synthesis for timeline-based gameshttps://zbmath.org/1530.682382024-04-15T15:10:58.286558Z"Acampora, Renato"https://zbmath.org/authors/?q=ai:acampora.renato"Geatti, Luca"https://zbmath.org/authors/?q=ai:geatti.luca"Gigante, Nicola"https://zbmath.org/authors/?q=ai:gigante.nicola"Montanari, Angelo"https://zbmath.org/authors/?q=ai:montanari.angelo"Picotti, Valentino"https://zbmath.org/authors/?q=ai:picotti.valentinoSummary: In the timeline-based approach to planning, originally born in the space sector, the evolution over time of a set of state variables (the timelines) is governed by a set of temporal constraints. Traditional timeline-based planning systems excel at the integration of planning with execution by handling \textit{temporal uncertainty}. In order to handle general nondeterminism as well, the concept of \textit{timeline-based games} has been recently introduced. It has been proved that finding whether a winning strategy exists for such games is \textsf{2EXPTIME}-complete. However, a concrete approach to synthesize controllers implementing such strategies is missing. This paper fills this gap, outlining an approach to controller synthesis for timeline-based games.
For the entire collection see [Zbl 1522.68028].Game theoretic security framework for quantum key distributionhttps://zbmath.org/1530.810562024-04-15T15:10:58.286558Z"Krawec, Walter O."https://zbmath.org/authors/?q=ai:krawec.walter-o"Miao, Fei"https://zbmath.org/authors/?q=ai:miao.feiSummary: In this paper, we propose a game-theoretic model of security for quantum key distribution (QKD) protocols. QKD protocols allow two parties to agree on a shared secret key, secure against an adversary bounded only by the laws of physics (as opposed to classical key distribution protocols which, by necessity, require computational assumptions to be placed on the power of an adversary). We investigate a novel framework of security using game theory where all participants (including the adversary) are rational. We will show that, in this framework, certain impossibility results for QKD in the standard adversarial model of security still remain true here. However, we will also show that improved key-rate efficiency is possible in our game-theoretic security model.
For the entire collection see [Zbl 1398.68017].Mobile payment, third-party payment platform entry and information sharing in supply chainshttps://zbmath.org/1530.900182024-04-15T15:10:58.286558Z"Fan, Xiaojun"https://zbmath.org/authors/?q=ai:fan.xiaojun"Zhao, Wenyu"https://zbmath.org/authors/?q=ai:zhao.wenyu"Zhang, Ting"https://zbmath.org/authors/?q=ai:zhang.ting.2|zhang.ting.4|zhang.ting"Yan, Endian"https://zbmath.org/authors/?q=ai:yan.endianSummary: With the development of information technology, increasing retailers cooperate with third-party payment platforms (3PPs) to provide mobile payment service for consumers. The entry of 3PPs into supply chains, not only changes the cash flow, but also decreases consumer price sensitivity and stimulates demand by facilitating credit consumptions. Moreover, information sharing becomes more feasible with the help of 3PPs. To study the impacts of 3PP entry, we build game-theoretic models in a supply chain consisting of a manufacturer, a retailer and a 3PP, and derive the equilibrium in both the non-information sharing and information sharing cases. We show that the 3PP should make a reasonable commission rate which can lure the retailer to introduce the 3PP as well as maintain the 3PP's profitability. The 3PP entry allows the retailer to set a higher price without decreasing the demand. However, to seize all of the benefit of the 3PP entry, the first mover manufacturer increases the wholesale price to a large extent. As a result, the 3PP entry causes a win-lose situation for the manufacturer and the retailer. The supply chain can be better off from the 3PP entry if it can significantly decrease consumer price sensitivity or its fixed investment cost is low. Furthermore, we find that information sharing benefits the manufacturer and the 3PP but harms the retailer. While information sharing always decreases the expected profit for the supply chain without the 3PP, it may increase that for the supply chain with the 3PP. To improve the supply chain profitability, we suggest to provide incentives for retailer information sharing if the 3PP can significantly decrease consumer price sensitivity (i.e., the proportion of the 3PP users is higher, the grace period of credit consumption is lower, or the cash opportunity cost is lower).Strategic information sharing in the dual-channel closed loop supply chain with nonlinear production costhttps://zbmath.org/1530.900262024-04-15T15:10:58.286558Z"Wang, Tong-Yuan"https://zbmath.org/authors/?q=ai:wang.tong-yuan"Chen, Zhen-Song"https://zbmath.org/authors/?q=ai:chen.zhensong"Wang, Xian-Jia"https://zbmath.org/authors/?q=ai:wang.xianjia"Govindan, Kannan"https://zbmath.org/authors/?q=ai:govindan.kannan"Skibniewski, Miroslaw J."https://zbmath.org/authors/?q=ai:skibniewski.miroslaw-jSummary: This paper explores the strategy of information sharing within a closed loop supply chain comprising three echelons and dual channels. By considering the supplier's collecting activities and the two formats of nonlinear production costs (\textit{i.e.}, production diseconomy and production economy) faced by the manufacturer, we construct and utilize game-theoretic models to determine the optimal strategy (\textit{i.e.}, no sharing, sharing information solely with the manufacturer, sharing with the supplier, and sharing with both the manufacturer and supplier) for information sharing by the retailer. The findings indicate that the retailer's inclination to voluntarily share information and the most effective approach are significantly influenced by the interplay between the supplier's recycling efficiency and the manufacturer's nonlinear production cost. Specifically, in the context of production diseconomy, it is commonly observed that the retailer can derive advantages by engaging in information sharing with a supplier who possesses a high recycling efficiency. In contract, the retailer would share the information when the recycling efficiency is high or the production economy coefficient is large. Otherwise, no sharing strategy can be considered as the optimal choice. Ultimately, the study aims to assess the effects of various approaches to sharing information on the remaining participants within the supply chain.Modeling of the city's transport network using game-theoretic methods on the example of Petrozavodskhttps://zbmath.org/1530.900302024-04-15T15:10:58.286558Z"Ermolin, Nikolay A."https://zbmath.org/authors/?q=ai:ermolin.nikolay-a"Khitraya, Vitalia A."https://zbmath.org/authors/?q=ai:khitraya.vitalia-a"Khitryi, Andrey V."https://zbmath.org/authors/?q=ai:khitryi.andrey-v"Mazalov, Vladimir V."https://zbmath.org/authors/?q=ai:mazalov.vladimir-viktorovich"Nikitina, Natalia N."https://zbmath.org/authors/?q=ai:nikitina.natalia-nSummary: The paper presents the results of modeling of the city's transport network. The effectiveness of the game-theoretic method for estimating the centrality of graph vertices using the Myerson value is demonstrated on the transport graph. Correspondences in the given graph are found with gravitational and entropy approaches, using the information about citizens and companies distributed by vertices in the graph. The results of computer calculations are represented on the transport network of the city of Petrozavodsk.
For the entire collection see [Zbl 1522.91009].A Lagrangian heuristics for balancing the average weighted completion times of two classes of jobs in a single-machine scheduling problemhttps://zbmath.org/1530.900362024-04-15T15:10:58.286558Z"Avolio, Matteo"https://zbmath.org/authors/?q=ai:avolio.matteo"Fuduli, Antonio"https://zbmath.org/authors/?q=ai:fuduli.antonioSummary: We tackle a new single-machine scheduling problem, whose objective is to balance the average weighted completion times of two classes of jobs. Because both the job sets contribute to the same objective function, this problem can be interpreted as a cooperative two-agent scheduling problem, in contraposition to the standard multiagent problems, which are of the competitive type since each class of job is involved only in optimizing its agent's criterion. Balancing the completion times of different sets of tasks finds application in many fields, such as in logistics for balancing the delivery times, in manufacturing for balancing the assembly lines and in services for balancing the waiting times of groups of people.
To solve the problem, for which we show the NP-hardness, a Lagrangian heuristic algorithm is proposed. In particular, starting from a nonsmooth variant of the quadratic assignment problem, our approach is based on the Lagrangian relaxation of a linearized model and reduces to solve a finite sequence of successive linear assignment problems. Numerical results are presented on a set of randomly generated test problems, showing the efficiency of the proposed technique.Game-theoretic approach to Hölder regularity for PDEs involving eigenvalues of the Hessianhttps://zbmath.org/1530.910112024-04-15T15:10:58.286558Z"Blanc, Pablo"https://zbmath.org/authors/?q=ai:blanc.pablo"Han, Jeongmin"https://zbmath.org/authors/?q=ai:han.jeongmin"Parviainen, Mikko"https://zbmath.org/authors/?q=ai:parviainen.mikko"Ruosteenoja, Eero"https://zbmath.org/authors/?q=ai:ruosteenoja.eeroSummary: We prove a local Hölder estimate for any exponent \(0<\delta <\frac{1}{2}\) for solutions of the dynamic programming principle
\[
\begin{array}{@{}rcl@{}}
u^{\varepsilon} (x) = \sum\limits_{j=1}^n \alpha_j \underset{\dim(S)=j}{\inf} \underset{|v|=1}{\underset{v\in S}{\sup}} \frac{u^{\varepsilon} (x + \varepsilon v) + u^{\varepsilon} (x - \varepsilon v)}{2}
\end{array}
\] with \(\alpha_1, \alpha_n > 0\) and \(\alpha_2,\cdots , \alpha_{n- 1} \geq 0\). The proof is based on a new coupling idea from game theory. As an application, we get the same regularity estimate for viscosity solutions of the PDE
\[
\sum\limits_{i=1}^n \alpha_i \lambda_i(D^2u)=0,
\]
where \(\lambda_1(D^2u) \leq \cdots \leq \lambda_n(D^2u)\) are the eigenvalues of the Hessian.Constrained contests with a continuum of battleshttps://zbmath.org/1530.910122024-04-15T15:10:58.286558Z"Hwang, Sung-Ha"https://zbmath.org/authors/?q=ai:hwang.sung-ha"Koh, Youngwoo"https://zbmath.org/authors/?q=ai:koh.youngwoo"Lu, Jingfeng"https://zbmath.org/authors/?q=ai:lu.jingfengSummary: We study a contest problem in which two players compete on a continuum of battlefields by spending resources subject to some constraints on their strategies. Following \textit{R. B. Myerson} [Am. Polit. Sci. Rev. 87, No. 4, 856--869 (1993; \url{doi:10.2307/2938819})], we assume that each player's resource allocation on each battlefield is an independent random draw from the same distribution. Within each battlefield, the player who allocates a higher level of resources wins, but both players incur costs for resource allocation. To analyze this problem, we introduce a systematic way to identify equilibrium allocation strategies and show that any equilibrium strategy of a player renders the rival indifferent in terms of the ``constraint-adjusted payoff''. Using this, we provide a complete characterization of equilibrium allocation strategies. We also show that whereas a symmetric budget constraint may induce players to spend more resources than in the case with no constraint, asymmetric budgets that are proportional to players' values of winning would eliminate this possibility.Buying winnershttps://zbmath.org/1530.910132024-04-15T15:10:58.286558Z"Louis-Sidois, Charles"https://zbmath.org/authors/?q=ai:louis-sidois.charlesSummary: Two principals with heterogeneous budgets compete to buy the best agent (the winner). First, the principals make initial offers to the agents before the winner is known. Then, if the winner has not accepted any offer, the principals make a second round of offers after the winner is revealed. In equilibrium, the principal with the higher budget offers her entire budget to the winner after he is revealed. The principal with the lower budget makes an offer to one agent before the winner is revealed. The timing of offers favors the high-budget principal: the low-budget principal faces adverse selection because only an agent with a low win probability accepts her offer. Moreover, the probability that the high-budget principal buys the winner increases with the number of agents. Finally, limiting pre-revelation offers favors the high-budget principal, while the opposite is true for post-revelation limits.The two-person and zero-sum matrix game with probabilistic linguistic informationhttps://zbmath.org/1530.910142024-04-15T15:10:58.286558Z"Mi, Xiaomei"https://zbmath.org/authors/?q=ai:mi.xiaomei"Liao, Huchang"https://zbmath.org/authors/?q=ai:liao.huchang"Zeng, Xiao-Jun"https://zbmath.org/authors/?q=ai:zeng.xiaojun"Xu, Zeshui"https://zbmath.org/authors/?q=ai:xu.zeshuiSummary: Game theory establishes mathematical models of strategic interactions among rational decision-makers. In many situations, the crisp values of payoffs are difficult to obtain while the probabilistic linguistic information is easy to collect. However, the existing research on matrix game did not consider the probabilistic linguistic information. To bridge this gap, this study takes the probabilistic linguistic information as the input of a two-person and zero-sum matrix game, and addresses the vague information by triangular membership functions. Such a two-person and zero-sum matrix game with probabilistic linguistic information is a useful technique for multiple criteria analysis. In addition, it outputs the same form of information as the inputs to increase the interpretability compared with other uncertain matrix games. An illustrative example about the forest management is provided to show the validity and advantages of the two-person and zero-sum matrix game with probabilistic linguistic information.Nash equilibria in random games with right fat-tailed distributionshttps://zbmath.org/1530.910152024-04-15T15:10:58.286558Z"Pei, Ting"https://zbmath.org/authors/?q=ai:pei.ting"Takahashi, Satoru"https://zbmath.org/authors/?q=ai:takahashi.satoruSummary: We study the distribution of the number of mixed strategy Nash equilibria in two-player games where each player's payoffs are independently drawn from an identical distribution. When the payoff distributions are sufficiently right fat-tailed, we characterize the Nash equilibria by best reply cycles of pure strategies, and we show that the expected number of Nash equilibria is approximately \(\sqrt{\pi mn/(m+n)}\) in a random \(m\times n\) asymmetric game and approximately \(n/2\) in a random \(n\times n\) symmetric game. We also provide new lower bounds for the expected number of Nash equilibria in a random game with any type of payoff distribution.Concept of social value orientation in measuring cooperative behavior incentive in gameshttps://zbmath.org/1530.910162024-04-15T15:10:58.286558Z"Xia, Yuyan"https://zbmath.org/authors/?q=ai:xia.yuyan"Li, Yin"https://zbmath.org/authors/?q=ai:li.yin|li.yin.1Summary: The purpose of this study is to explore the effects and mechanisms of cooperation indicators such as interpersonal trust, social preferences, and social value orientations on cooperative behavior, and we develop a psychologically grounded model of trust-based cooperation. Some accounts of cooperation in product choice games have focused on developing simple indicators of game severity i.e., the extent to which the game facilitates noncooperative choices that are derived exclusively from the game's payoff structure. However, this approach does not provide a clear explanation of the psychological mechanisms why the game's payoffs affect the rate of cooperation. When considering individuals' social preferences and positive expectations (beliefs) for how to predict the emergence of trust-based cooperation as an expected utility maximizing strategy, we show a simple decision model for trust-based cooperation. In addition, we show how these predictions are associated with a game-specific cooperation index. We then describe under what conditions trust-based cooperation is rationalizable and how trust-based decisions can be understood through the interplay between of payoffs, preferences, and beliefs.
For the entire collection see [Zbl 1522.91009].Social roles and competitiveness: my willingness to compete depends on who I am (supposed to be)https://zbmath.org/1530.910172024-04-15T15:10:58.286558Z"Zhang, Peilu"https://zbmath.org/authors/?q=ai:zhang.peilu"Zhang, Yinjunjie"https://zbmath.org/authors/?q=ai:zhang.yinjunjie"Palma, Marco A."https://zbmath.org/authors/?q=ai:palma.marco-aSummary: Women frequently react less favorably to competition than men. In this paper, we investigate the effects of social roles on willingness to compete (WTC). Subjects compete in two-person teams. In the treatment, one team member is randomly assigned the role of ``breadwinner/manager'', and the other person is randomly assigned as the ``supporter/assistant''. The only difference between the roles is the labels. In the baseline, subjects compete without any role assignment. We find women's WTC increases by 41\% (44\%) when they are assigned as breadwinners (managers) compared to women in the baseline. Men have lower WTC when they are assigned as supporters or assistants. There is no gender gap in WTC in treatment groups. Social norms of competitiveness for each role are elicited, and are suggested as the main driver of changes in WTC by the role assignment. We also examine other potential mechanisms through which social roles affect WTC.Heterogeneous multi-player imitation learninghttps://zbmath.org/1530.910182024-04-15T15:10:58.286558Z"Lian, Bosen"https://zbmath.org/authors/?q=ai:lian.bosen"Xue, Wenqian"https://zbmath.org/authors/?q=ai:xue.wenqian"Lewis, Frank L."https://zbmath.org/authors/?q=ai:lewis.frank-l(no abstract)Nash conditional independence curvehttps://zbmath.org/1530.910192024-04-15T15:10:58.286558Z"Portakal, Irem"https://zbmath.org/authors/?q=ai:portakal.irem"Sendra-Arranz, Javier"https://zbmath.org/authors/?q=ai:sendra-arranz.javierSummary: We study the Spohn conditional independence (CI) variety \(C_X\) of an \(n\)-player game \(X\) for undirected graphical models on \(n\) binary random variables consisting of one edge. For a generic game, we show that \(C_X\) is a smooth irreducible complete intersection curve (Nash conditional independence curve) in the Segre variety \((\mathbb{P}^1 )^{n-2} \times \mathbb{P}^3\) and we give an explicit formula for its degree and genus. We prove two universality theorems for \(C_X\): The product of any affine real algebraic variety with the real line or any affine real algebraic variety in \(\mathbb{R}^m\) defined by at most \(m-1\) polynomials is isomorphic to an affine open subset of \(C_X\) for some game \(X\).A canonical game -- 75 years in the making -- showing the equivalence of matrix games and linear programminghttps://zbmath.org/1530.910202024-04-15T15:10:58.286558Z"Brooks, Benjamin"https://zbmath.org/authors/?q=ai:brooks.benjamin"Reny, Philip J."https://zbmath.org/authors/?q=ai:reny.philip-jSummary: According to \textit{G. B. Dantzig} [Econometrica 17, 200--211 (1949; Zbl 0037.37305)], von Neumann was the first to observe that for any finite two-person zero-sum game, there is a feasible linear programming (LP) problem whose saddle points yield equilibria of the game, thus providing an immediate proof of the minimax theorem from the strong duality theorem. We provide an analogous construction going in the other direction. For any LP problem, we define a game and, with a brief and elementary proof, show that \textit{every} equilibrium either yields a saddle point of the LP problem or certifies that one of the primal or dual programs is infeasible and the other is infeasible or unbounded. We thus obtain an immediate proof of the strong duality theorem from the minimax theorem. Taken together, von Neumann's and our results provide a succinct and elementary demonstration that matrix games and linear programming are ``equivalent'' in a classical sense.A stochastic variant of replicator dynamics in zero-sum games and its invariant measureshttps://zbmath.org/1530.910212024-04-15T15:10:58.286558Z"Engel, Maximilian"https://zbmath.org/authors/?q=ai:engel.maximilian"Piliouras, Georgios"https://zbmath.org/authors/?q=ai:piliouras.georgiosSummary: We study the behavior of a stochastic variant of replicator dynamics in two-agent zero-sum games. Inspired by the well studied deterministic replicator equation, this model gives arguably a more realistic description of real world settings and, as we demonstrate here, exhibits totally distinct behavior when compared to its deterministic counterpart which is known to be recurrent. In more detail, we characterize the statistics of such systems by their invariant measures which can be shown to be entirely supported on the boundary of the space of mixed strategies. Depending on the noise strength we can furthermore characterize these invariant measures by finding accumulation of mass at specific parts of the boundary. In particular, regardless of the magnitude of noise, we show that any invariant probability measure is a convex combination of Dirac measures on pure strategy profiles, which correspond to vertices/corners of the agents' simplices. Thus, in the presence of stochastic perturbations, even in the most classic zero-sum settings, such as Matching Pennies, we observe a stark disagreement between the axiomatic prediction of Nash equilibrium and the evolutionary emergent behavior derived by an assumption of stochastically adaptive, learning agents.The \(n\)-player Hirshleifer contesthttps://zbmath.org/1530.910222024-04-15T15:10:58.286558Z"Ewerhart, Christian"https://zbmath.org/authors/?q=ai:ewerhart.christian"Sun, Guang-Zhen"https://zbmath.org/authors/?q=ai:sun.guangzhenSummary: While the game-theoretic analysis of conflict is often based on the assumption of multiplicative noise, additive noise such as considered by \textit{J. Hirshleifer}
[Public Choice 63, 101--112 (1989; \url{doi:10.1007/BF00153394})] may be equally plausible depending on the application. In this paper, we examine the equilibrium set of the \(n\)-player difference-form contest with heterogeneous valuations. For high and intermediate levels of noise, the equilibrium is in pure strategies, with at most one player being active. For small levels of noise, however, we find a variety of equilibria in which some but not necessarily all players randomize. In the case of homogeneous valuations, we obtain a partial uniqueness result for symmetric equilibria. As the contest becomes increasingly decisive, at least two contestants bid up to the valuation of the second-ranked contestant, while any others ultimately drop out. Thus, in the limit, equilibria of the Hirshleifer contest share important properties of equilibria of the corresponding all-pay auction.Complete-rent-dissipation contest designhttps://zbmath.org/1530.910232024-04-15T15:10:58.286558Z"Kawamori, Tomohiko"https://zbmath.org/authors/?q=ai:kawamori.tomohikoSummary: We consider contest success functions (CSFs) that exhibit complete rent dissipation. If the prize values are observable by the contest designer, for any value tuple, we show that there exists a CSF that exhibits complete dissipation in any equilibrium if and only if the number of contestants is greater than or equal to three or the values are homogeneous. If the values are unobservable by the contest designer, we show that there exists no CSF that exhibits complete dissipation in some equilibrium for any value tuple.Sequential formation of alliances in survival contestshttps://zbmath.org/1530.910242024-04-15T15:10:58.286558Z"Konishi, Hideo"https://zbmath.org/authors/?q=ai:konishi.hideo"Pan, Chen-Yu"https://zbmath.org/authors/?q=ai:pan.chen-yuSummary: We consider a \textit{sequential formation} of alliances à la \textit{F. Bloch} [Games Econ. Behav. 14, No. 1, 90--123 (1996; Zbl 0862.90143)] and \textit{A. Okada} [Games Econ. Behav. 16, No. 1, 97--108 (1996; Zbl 0873.90125)], followed by a two-stage contest in which alliances first compete with each other, and then the members in the winning alliance compete again for an indivisible prize. In contrast to \textit{H. Konishi} and \textit{C.-Y. Pan} [Journal of Economic Behavior \& Organization 189, 337--358 (2021; \url{doi:10.1016/j.jebo.2021.06.039})], which adopted an \textit{open-membership} game as the alliance formation process, alliances are allowed to limit their memberships (excludable alliances). We show that if members' efforts are strongly complementary to each other, there will be exactly two asymmetric alliances: the larger alliance is formed first and then the remaining players form the smaller one. This result contrasts with the one under open membership, where moderate complementarity is necessary to support a two-alliance structure. It is also in stark contrast with \textit{F. Bloch} et al. [Economics of Governance 7, No. 1, 3--29 (2006; \url{doi:10.1007/s10101-005-0099-9})], which shows that a grand coalition is formed in the same game if the prize is divisible and a binding contract can be used to avoid further conflicts after an alliance wins the prize.
{{\copyright} 2019 IAET}Discrete Colonel Blotto games with two battlefieldshttps://zbmath.org/1530.910252024-04-15T15:10:58.286558Z"Liang, Dong"https://zbmath.org/authors/?q=ai:liang.dong|liang.dong.1"Wang, Yunlong"https://zbmath.org/authors/?q=ai:wang.yunlong"Cao, Zhigang"https://zbmath.org/authors/?q=ai:cao.zhigang"Yang, Xiaoguang"https://zbmath.org/authors/?q=ai:yang.xiaoguangSummary: The Colonel Blotto game is one of the most classical zero-sum games, with diverse applications in auctions, political elections, etc. We consider the discrete two-battlefield Colonel Blotto game, a basic case that has not yet been completely characterized. We study three scenarios where at least one player's resources are indivisible (discrete), and compare them with a benchmark scenario where the resources of both players are arbitrarily divisible (continuous). We present the equilibrium values for all three scenarios, and provide a complete equilibrium characterization for the scenario where both players' resources are indivisible. Our main finding is that, somewhat surprisingly, the distinction between continuous and discrete strategy spaces generally has no effect on players' equilibrium values. In some special cases, however, the larger continuous strategy space when resources are divisible does bring the corresponding player a higher equilibrium value than when resources are indivisible, and this effect is more significant for the stronger player who possesses more resources than for the weaker player.Fixing knockout tournaments with seedshttps://zbmath.org/1530.910262024-04-15T15:10:58.286558Z"Manurangsi, Pasin"https://zbmath.org/authors/?q=ai:manurangsi.pasin"Suksompong, Warut"https://zbmath.org/authors/?q=ai:suksompong.warutSummary: Knockout tournaments constitute a popular format for organizing sports competitions. While prior results have shown that it is often possible to manipulate a knockout tournament by fixing the bracket, these results ignore the prevalent aspect of player seeds, which can significantly constrain the chosen bracket. We show that certain structural conditions that guarantee that a player can win a knockout tournament without seeds are no longer sufficient in light of seed constraints. On the other hand, we prove that when the pairwise match outcomes are generated randomly, all players are still likely to be knockout winners under the same probability threshold with seeds as without seeds. In addition, we investigate the complexity of deciding whether a manipulation is possible when seeds are present.Is there free riding in group contests?https://zbmath.org/1530.910272024-04-15T15:10:58.286558Z"Sela, Aner"https://zbmath.org/authors/?q=ai:sela.anerSummary: We study best-of-two contests between two symmetric groups of players. Each group includes \(n\) heterogeneous players who have resource budgets that decrease in the second stage proportionally to the resource allocated in the first stage. We demonstrate that in our group contests complete ``free riding'' does not necessarily exist, namely, there is always a subgame perfect equilibrium in which either all the players in a group allocate positive resources in both stages or just some of them, but never only one player allocates a resource in any stage when all the others in his group are free riders.Nash equilibrium seeking with prescribed performancehttps://zbmath.org/1530.910282024-04-15T15:10:58.286558Z"Sun, Chao"https://zbmath.org/authors/?q=ai:sun.chao"Hu, Guoqiang"https://zbmath.org/authors/?q=ai:hu.guoqiang(no abstract)On sustainable equilibriahttps://zbmath.org/1530.910292024-04-15T15:10:58.286558Z"Govindan, Srihari"https://zbmath.org/authors/?q=ai:govindan.srihari"Laraki, Rida"https://zbmath.org/authors/?q=ai:laraki.rida"Pahl, Lucas"https://zbmath.org/authors/?q=ai:pahl.lucasSummary: Following the ideas laid out in [\textit{R. B. Myerson}, in: Understanding strategic interaction. Essays in honor of Reinhard Selten. Berlin: Springer. 111--121 (1996; Zbl 0876.90091); \textit{J. Hofbauer}, ``Some thoughts on sustainable/learnable equilibria'', in: Conference Book of the XV Italian Meeting of Game Theory and Applications. Universitá degli Studi di Urbino (2003)] defined a Nash equilibrium of a finite game as sustainable if it can be made the unique Nash equilibrium of a game obtained by deleting/adding a subset of the strategies that are inferior replies to it. This paper proves a result about sustainable equilibria and uses it to provide a refinement as well. Our result concerns the Hofbauer-Myerson conjecture about the relationship between the sustainability of an equilibrium and its index: for a generic class of games, an equilibrium is sustainable iff its index is +1. \textit{A. von Schemde} and \textit{B. von Stengel} [Lect. Notes Comput. Sci. 4997, 242--254 (2008; Zbl 1136.91344)] proved this conjecture for bimatrix games; we show that the conjecture is true for all finite games. More precisely, we prove that an equilibrium is isolated and has index +1 if and only if it can be made unique in a larger game obtained by adding finitely many strategies that are inferior replies to that equilibrium. It follows in a straightforward way from our result that sustainable equilibria fail the decomposition axiom for games as formulated by \textit{J.-F. Mertens} [Math. Oper. Res. 14, No. 4, 575--625 (1989; Zbl 0687.90097)]. In order to rectify this problem we propose a refinement, called strongly sustainable equilibria, which is shown to exist for all regular games.Perfect regular equilibriumhttps://zbmath.org/1530.910302024-04-15T15:10:58.286558Z"Jung, Hanjoon Michael"https://zbmath.org/authors/?q=ai:jung.hanjoon-michaelSummary: We extend the solution concept of perfect Bayesian equilibrium to general games that allow a continuum of types and strategies. In finite games, a perfect Bayesian equilibrium is weakly consistent and a subgame perfect Nash equilibrium. In general games, however, it might not satisfy these criteria. To solve this problem, we revise the definition of perfect Bayesian equilibrium by replacing Bayes' rule with regular conditional probability. The revised solution concept is referred to as perfect regular equilibrium. We present the conditions that ensure the existence of this equilibrium. Then we show that every perfect regular equilibrium is always weakly consistent and a subgame perfect Nash equilibrium, and is equivalent to a simple version of perfect Bayesian equilibrium in a finite game.
{{\copyright} IAET}The in-group egalitarian Owen valueshttps://zbmath.org/1530.910312024-04-15T15:10:58.286558Z"Abe, Takaaki"https://zbmath.org/authors/?q=ai:abe.takaaki"Nakada, Satoshi"https://zbmath.org/authors/?q=ai:nakada.satoshiSummary: This paper proposes a new class of allocation rules, which is referred to as \textit{the in-group egalitarian Owen values}, that integrates two seemingly conflicting principles -- marginalism and egalitarianism -- in the framework of cooperative games with coalition structures. This class of allocation rules facilitates the use of different principles of allocation in different layers of a social structure such as allocation across coalitions and within a coalition. Therefore, each coalition can employ its specific distributive principle for intra-coalition distribution. Our main results provide axiomatic foundations for the class of allocation rules, in which monotonicity properties highlight the importance of the proposed solutions. We also show that various monotonicity properties generate various allocation rules, where the Owen value and the in-group egalitarian division value are special cases. These results extend the egalitarian Shapley values to the games with coalition structures and offer a rationale for monotonic allocation rules in the presence of social structures.The \(\tau\)-value in multistage games with pairwise interactionshttps://zbmath.org/1530.910322024-04-15T15:10:58.286558Z"Bulgakova, Mariia A."https://zbmath.org/authors/?q=ai:bulgakova.mariia-aSummary: We consider multistage bimatrix games with pairwise interactions. On the first stage players chose their neighbours and formed a network. On the later stages bimatrix games between neighbours by network take places. As a solution consider the \(\tau\)-value ([\textit{S. H. Tijs}, Math. Soc. Sci. 13, 177--181 (1987; Zbl 0617.90095)]). Earlier we calculated coefficient \(\lambda\) of \(\tau\)-value in case of two-stage game. Now we consider a general case of one-stage game with any players and any number of links. We assumed followings: \(N\) is set of players, \(|N|\ge 2\) and any type of network \(g\). It is also assumed, that there are not necessarily paths between every pair of vertices. We will consider conditions for time-consistency of \(\tau\)-value in two-stage game.
For the entire collection see [Zbl 1522.91009].Null players, outside options, and stability: the conditional Shapley valuehttps://zbmath.org/1530.910332024-04-15T15:10:58.286558Z"Casajus, André"https://zbmath.org/authors/?q=ai:casajus.andre"La Mura, Pierfrancesco"https://zbmath.org/authors/?q=ai:la-mura.pierfrancescoSummary: We suggest a new component efficient solution for monotonic TU games with a coalition structure, the conditional Shapley value. In contrast to other such solutions, it satisfies the null player property. Nevertheless, it accounts for the players' outside options in productive components of coalition structures. For all monotonic games, there exist coalition structures that are stable under the conditional Shapley value. For voting games, such stable coalition structures support Gamson's theory of coalition formation [\textit{W. Gamson}, Am. Sociol. Rev. 26, No. 3, 373--382 (1961; \url{doi:10.2307/2090664})].Stability and welfare in (dichotomous) hedonic diversity gameshttps://zbmath.org/1530.910342024-04-15T15:10:58.286558Z"Darmann, Andreas"https://zbmath.org/authors/?q=ai:darmann.andreasSummary: In a hedonic diversity game (HDG) there are two types of agents (red and blue agents) that need to form disjoint coalitions, i.e., subgroups of agents. Each agent's preferences over the coalitions depend on the relative number of agents of the same type in her coalition. In the special case of a dichotomous hedonic diversity game (DHDG) each agent distinguishes between approved and disapproved fractions only. We aim at outcomes that are stable against agents' deviations, and at outcomes that maximize social welfare. In particular, we show that the strict core of a DHDG may be empty even in instances with only three agents, while each HDG with two agents has a non-empty strict core. We also provide several computational complexity results for DHDGs with respect to the number of fractions approved per agent. For instance, we prove that deciding whether a DHDG has a non-empty strict core is \(\mathsf{NP}\)-complete even when each agent approves of at most three fractions. In addition, we show that deciding whether a DHDG admits a Nash stable outcome is \(\mathsf{NP}\)-complete even in restricted settings with only two approved fractions per agent -- therewith, improving a result in the literature. For the task of maximizing social welfare, we apply approval scores and Borda scores from voting theory. For DHDGs and approval scores, we draw the sharp separation line between polynomially solvable and \(\mathsf{NP}\)-complete cases with respect to the fixed number of approved fractions per agent. We complement these findings with an \(\mathsf{NP}\)-completeness result for HDGs under Borda scores.Hedonic diversity games: a complexity picture with more than two colorshttps://zbmath.org/1530.910352024-04-15T15:10:58.286558Z"Ganian, Robert"https://zbmath.org/authors/?q=ai:ganian.robert"Hamm, Thekla"https://zbmath.org/authors/?q=ai:hamm.thekla"Knop, Dušan"https://zbmath.org/authors/?q=ai:knop.dusan"Schierreich, Šimon"https://zbmath.org/authors/?q=ai:schierreich.simon"Suchý, Ondřej"https://zbmath.org/authors/?q=ai:suchy.ondrejSummary: Hedonic diversity games are a variant of the classical hedonic games designed to better model a variety of questions concerning diversity and fairness. Previous works mainly targeted the case with two diversity classes (represented as colors in the model) and provided some initial complexity-theoretic and existential results concerning Nash and individually stable outcomes. Here, we design new algorithms accompanied with lower bounds which provide a comprehensive parameterized-complexity picture for computing Nash and individually stable outcomes with respect to the most natural parameterizations of the problem. Crucially, our results hold for general hedonic diversity games where the number of colors is not necessarily restricted to two, and show that -- apart from two trivial cases -- a necessary condition for tractability in this setting is that the number of colors is bounded by the parameter. Moreover, for the special case of two colors we resolve an open question asked in previous work [\textit{N. Boehmer} and \textit{E. Elkind}, ``Individual-based stability in hedonic diversity games'', Preprint, \url{arXiv:1911.08669}].Robust equilibria in tournamentshttps://zbmath.org/1530.910362024-04-15T15:10:58.286558Z"Han, Lining"https://zbmath.org/authors/?q=ai:han.lining"Juarez, Ruben"https://zbmath.org/authors/?q=ai:juarez.ruben"Vargas, Miguel"https://zbmath.org/authors/?q=ai:vargas.miguelSummary: We study robust equilibria in tournaments, where agents endowed with power form coalitions, and the coalition formed with the highest power prevails. We introduce the \textit{no-threat equilibrium} (NTE), a stable partition where if a coalition deviates, then a new coalition could counter by forming an even stronger coalition. The NTE exists for any power function and preferences if and only if the set of feasible coalitions is a `Helly' family.
In contrast, the \textit{core} is a partition in which no group of agents can profitably deviate by forming a feasible coalition, assuming that other agents do not react to such a deviation. The core is not empty for any power function and preferences if and only if the set of feasible coalitions has a `hierarchical-structure'.
The paper also adapts and characterizes other stability concepts to tournaments, including the \(\alpha\)-\textit{core}, \(\beta\)-\textit{core}, \textit{farsighted core} and \textit{bargaining set}.Second-language acquisition behavior and hegemonic languagehttps://zbmath.org/1530.910372024-04-15T15:10:58.286558Z"Hatsumi, Kentaro"https://zbmath.org/authors/?q=ai:hatsumi.kentaroSummary: We construct a game-theoretic model in which there are multiple countries with their own languages and each citizen can gain from additional communication in her secondarily acquired language. We demonstrate that in any equilibrium, a hegemonic language, which is a language that all citizens in other countries want to study, emerges. Such an equilibrium is more likely to exist if the size of the population of a country that is not the largest increases, or if the ratio of the gain from the additional communication in the second language to the cost of acquisition increases.
{{\copyright} 2022 IAET}Pareto efficiency of finite-horizon mean-field cooperative stochastic differential games with Poisson jumpshttps://zbmath.org/1530.910382024-04-15T15:10:58.286558Z"Hu, Po"https://zbmath.org/authors/?q=ai:hu.po"Ma, Hongbin"https://zbmath.org/authors/?q=ai:ma.hongbinSummary: This paper investigates finite-horizon mean-field cooperative stochastic differential games (CSDG) with Poisson jumps. The game model can describe the case where the game has external disturbances and suffers sudden changes. First, for the fixed initial state, the necessary conditions which guarantee the existence of Pareto solutions can be obtained by utilizing the Lagrange multiplier method and the mean-field type stochastic maximum principle (MF-SMP) with Poisson jumps. Then, the sufficient conditions which guarantee the existence of Pareto efficient strategies are derived. Next, for any initial states, the well-posedness of finite-horizon mean-field CSDG with Poisson jumps is established under the assumption that the solution of generalized algebraic Riccati equations (GAREs) exists. Further, all Pareto solutions can be obtained by constructing an algebraic Lyapunov equations (ALEs). Finally, a numerical example given illustrates our results.Asymmetric majority pillage gameshttps://zbmath.org/1530.910392024-04-15T15:10:58.286558Z"Kerber, Manfred"https://zbmath.org/authors/?q=ai:kerber.manfred"Rowat, Colin"https://zbmath.org/authors/?q=ai:rowat.colin"Yoshihara, Naoki"https://zbmath.org/authors/?q=ai:yoshihara.naokiSummary: We study pillage games [\textit{J. S. Jordan}, J. Econ. Theory 131, No. 1, 26--44 (2006; Zbl 1142.91018)], which model unstructured power contests. To enable empirical tests of pillage game theory, we relax a symmetry assumption that agents' intrinsic contributions to a coalition's power is identical. We characterise the core for all \(n\). In the three-agent game: (i) only eight configurations are possible for the core, which contains at most six allocations; (ii) for each core configuration, the stable set is either unique or fails to exist; (iii) the linear power function creates a tension between a stable set's existence and the interiority of its allocations, so that only special cases contain strictly interior allocations. Our analysis suggests that non-linear power functions may offer better empirical tests of pillage game theory.A union self-evaluation approach to associated consistency for cooperative gameshttps://zbmath.org/1530.910402024-04-15T15:10:58.286558Z"Li, Wenzhong"https://zbmath.org/authors/?q=ai:li.wenzhong"Xu, Genjiu"https://zbmath.org/authors/?q=ai:xu.genjiu"van den Brink, René"https://zbmath.org/authors/?q=ai:van-den-brink.reneSummary: \textit{G. Xu} et al. [Linear Algebra Appl. 430, No. 11--12, 2896--2897 (2009; Zbl 1163.91010)] introduced the notion of associated consistency according to the idea of ``individual self-evaluation''. In this paper, we introduce a new type of associated consistency according to the idea of ``union self-evaluation'' instead of ``individual self-evaluation''. Adopting this type of associated consistency, we provide new axiomatizations of the equal allocation of non-separable contributions (EANSC) value and the center-of-gravity of the imputation set (CIS) value. Moreover, a dynamic process is given based on the type of associated games, which leads to the CIS value and EANSC value, starting from an arbitrary efficient payoff vector.The potential and consistency of the Owen value for fuzzy cooperative games with a coalition structurehttps://zbmath.org/1530.910412024-04-15T15:10:58.286558Z"Li, Zijun"https://zbmath.org/authors/?q=ai:li.zijun"Meng, Fanyong"https://zbmath.org/authors/?q=ai:meng.fanyongSummary: This paper extends the potential function and consistency to the Owen value for fuzzy cooperative games with a coalition structure. First, we prove that the unique payoff index satisfying the potential function is the Owen value. Then, we characterize the Owen value for fuzzy cooperative games with a coalition structure by fuzzy balanced contributions and fuzzy consistency, respectively. Finally, an example in supply chain is given to illustrate the relationship between the Owen value and potential function for fuzzy cooperative games with a coalition structure and solve the problem of payoff distribution in supply chain under fuzzy environment.Minimal balanced collections and their application to core stability and other topics of game theoryhttps://zbmath.org/1530.910422024-04-15T15:10:58.286558Z"Mermoud, Dylan Laplace"https://zbmath.org/authors/?q=ai:mermoud.dylan-laplace"Grabisch, Michel"https://zbmath.org/authors/?q=ai:grabisch.michel"Sudhölter, Peter"https://zbmath.org/authors/?q=ai:sudholter.peterSummary: Minimal balanced collections are a generalization of partitions of a finite set of \(n\) elements and have important applications in cooperative game theory and discrete mathematics. However, their number is not known beyond \(n = 4\). In this paper we investigate the problem of generating minimal balanced collections and implement the Peleg algorithm, permitting to generate all minimal balanced collections till \(n = 7\). Secondly, we provide practical algorithms to check many properties of coalitions and games, based on minimal balanced collections, in a way which is faster than linear programming-based methods. In particular, we construct an algorithm to check if the core of a cooperative game is a stable set in the sense of von Neumann and Morgenstern. The algorithm implements a theorem according to which the core is a stable set if and only if a certain nested balancedness condition is valid. The second level of this condition requires generalizing the notion of balanced collection to balanced sets.Cooperation in problems of common-pool resourceshttps://zbmath.org/1530.910432024-04-15T15:10:58.286558Z"Ordaz-Cuevas, Jesús Erubiel"https://zbmath.org/authors/?q=ai:ordaz-cuevas.jesus-erubiel"Sánchez-Pérez, Joss"https://zbmath.org/authors/?q=ai:sanchez-perez.joss-erickSummary: In this work we study problems of common-pool resources from a cooperative point of view. In particular we analyse whether it is possible for agents to agree to form a coalition to coordinate their level of appropriation and thus, avoid the tragedy of the commons. For this purpose, we investigate how agents in a coalition choose their joint level of appropriation (depending on the behavior of appropriators outside such coalition). Finally, we propose a way of associating with each problem (of common-pool resources) a game with externalities and studied its core.Braess' paradox: a cooperative game-theoretic point of viewhttps://zbmath.org/1530.910442024-04-15T15:10:58.286558Z"Passacantando, Mauro"https://zbmath.org/authors/?q=ai:passacantando.mauro"Gnecco, Giorgio"https://zbmath.org/authors/?q=ai:gnecco.giorgio"Hadas, Yuval"https://zbmath.org/authors/?q=ai:hadas.yuval"Sanguineti, Marcello"https://zbmath.org/authors/?q=ai:sanguineti.marcelloSummary: Braess' paradox is a classical result in the theory of congestion games. It motivates theoretically why adding a resource (e.g., an arc) to a network may sometimes worsen, rather than improve, the overall network performance. Differently from previous literature, which studies Braess' paradox in a non-cooperative game-theoretic setting, in this work, a framework is proposed to investigate its occurrence by exploiting cooperative games with transferable utility (TU games) on networks. In this way, instead of focusing on the marginal contribution to the network utility provided by the insertion of an arc when a single initial scenario is considered, the arc average marginal utility with respect to various initial scenarios, that is, its Shapley value in a suitably-defined TU game, is evaluated. It is shown that, for choices of the utility function of the TU game modeling congestion, there are cases for which the Shapley value associated with an arc is negative, meaning that its average marginal contribution to the network utility is negative.
{{\copyright} 2021 Wiley Periodicals LLC.}Influence relation in two-output multichoice voting gameshttps://zbmath.org/1530.910452024-04-15T15:10:58.286558Z"Siani, Joseph"https://zbmath.org/authors/?q=ai:siani.joseph"Tedjeugang, Narcisse"https://zbmath.org/authors/?q=ai:tedjeugang.narcisse"Tchantcho, Bertrand"https://zbmath.org/authors/?q=ai:tchantcho.bertrandSummary: The influence relation, defined within the set of simple games, is identified as a preorder. Additionally, it is proved to be a subpreorder of the preorders induced by the Shapley-Shubik and Banzhaf-Coleman indices. When this relation extends to voting games with abstention, detailed in [\textit{B. Tchantcho} et al., Games Econ. Behav. 64, No. 1, 335--350 (2008; Zbl 1153.91393)], and further to multichoice voting games as in [\textit{R. Pongou} et al., Oper. Res. Perspect. 1, No. 1, 42--49 (2014; \url{doi:10.1016/j.orp.2014.06.002})], it is shown that these extensions aren't always preorders. Even when they are, they don't necessarily align with the preorders induced by the extended Banzhaf-Coleman and Shapley-Shubik power indices in [\textit{J. Freixas}, Decis. Support Syst. 39, No. 2, 185--195 (2005; \url{doi:10.1016/j.dss.2003.10.006}); Ann. Oper. Res. 137, 45--66 (2005; Zbl 1138.91385)]. In this paper, we introduce extensions for two-output multichoice voting games that are both preorders and subpreorders of the Banzhaf-Coleman power index defined in Freixas [loc. cit.]. Further, we characterize the two-output multichoice voting games for which one of these new power theories agrees with the generalized Banzhaf-Coleman and Shapley-Shubik power indices in [\textit{J. Freixas}, Decis. Support Syst. 39, No. 2, 185--195 (2005; \url{doi:10.1016/j.dss.2003.10.006}); Ann. Oper. Res. 137, 45--66 (2005; Zbl 1138.91385)] respectively.Existence of stable coalition structures in three-player games with graph-constrained solutionhttps://zbmath.org/1530.910462024-04-15T15:10:58.286558Z"Sun, Ping"https://zbmath.org/authors/?q=ai:sun.ping.3|sun.ping|sun.ping.2|sun.ping.1Summary: The stability of coalition structures is investigated in the sense that no player prefers to individually deviate from the current coalition considering his utility. This principle is close to the concept of the Nash equilibrium. The evaluation of each player's utility is determined with respect to the solution concept -- the Shapley value with exogenous directed graph constraint. The existence of a stable coalition structure with respect to such a solution is examined for two-player as well as three-player games.
For the entire collection see [Zbl 1522.91009].Dynamic cost-sharing game with spanning arborescencehttps://zbmath.org/1530.910472024-04-15T15:10:58.286558Z"Ye, Peichen"https://zbmath.org/authors/?q=ai:ye.peichen"Li, Yin"https://zbmath.org/authors/?q=ai:li.yin.1"Petrosian, Ovanes"https://zbmath.org/authors/?q=ai:petrosyan.ovanes-lSummary: This paper presents the dynamic Shapley value for cost-sharing game with spanning arborescence. The cooperative behaviour of players is determined, and a two-stage directed network game is considered. At each stage, a cost matrix associated with the directed network is defined by players adopting strategies, and a minimum cost spanning arborescence on the directed network is determined. After the first stage, a particular player will leave the game with a certain probability, which depends on all players' behaviours in the first stage. The characteristic function is defined. Using the imputation distribution procedure (IDP), the dynamic Shapley value in the game is constructed.
For the entire collection see [Zbl 1522.91009].Submixing and shift-invariant stochastic gameshttps://zbmath.org/1530.910482024-04-15T15:10:58.286558Z"Gimbert, Hugo"https://zbmath.org/authors/?q=ai:gimbert.hugo"Kelmendi, Edon"https://zbmath.org/authors/?q=ai:kelmendi.edonSummary: We study optimal strategies in two-player stochastic games that are played on a finite graph, equipped with a general payoff function. The existence of optimal strategies that do not make use of memory and randomisation is a desirable property that vastly simplifies the algorithmic analysis of such games. Our main theorem gives a sufficient condition for the maximizer to possess such a simple optimal strategy. The condition is imposed on the payoff function, saying the payoff does not depend on any finite prefix (shift-invariant) and combining two trajectories does not give higher payoff than the payoff of the parts (submixing). The core technical property that enables the proof of the main theorem is that of the existence of \(\epsilon\)-subgame-perfect strategies when the payoff function is shift-invariant. Furthermore, the same techniques can be used to prove a finite-memory transfer-type theorem: namely that for shift-invariant and submixing payoff functions, the existence of optimal finite-memory strategies in one-player games for the minimizer implies the existence of the same in two-player games. We show that numerous classical payoff functions are submixing and shift-invariant.Optimal linear strategy for stochastic games with one-side control-sharing informationhttps://zbmath.org/1530.910492024-04-15T15:10:58.286558Z"Ju, Peijun"https://zbmath.org/authors/?q=ai:ju.peijun"Li, Xiaoqian"https://zbmath.org/authors/?q=ai:li.xiaoqian"Lei, Jing"https://zbmath.org/authors/?q=ai:lei.jing.1"Li, Tongxing"https://zbmath.org/authors/?q=ai:li.tongxing.2|li.tongxingSummary: We study a class of two-player finite-horizon linear-quadratic difference games with partial information and the control information is only one-side sharing. Specifically, the players' measurements are private information, and only one player is able to observe the other one's control information, but not inverse. By using the dynamic programming method, an optimal linear strategy profile is provided, which is in terms of decoupled and symmetric Riccati equations. Finally, a numerical example is given to illustrate our results.Markovian persuasion with two stateshttps://zbmath.org/1530.910502024-04-15T15:10:58.286558Z"Ashkenazi-Golan, Galit"https://zbmath.org/authors/?q=ai:ashkenazi-golan.galit"Hernández, Penélope"https://zbmath.org/authors/?q=ai:hernandez.penelope"Neeman, Zvika"https://zbmath.org/authors/?q=ai:neeman.zvika"Solan, Eilon"https://zbmath.org/authors/?q=ai:solan.eilonSummary: This paper addresses the question of how to best communicate information over time in order to influence an agent's belief and induced actions in a model with a binary state of the world that evolves according to a Markov process, and with a finite number of actions. We characterize the sender's optimal message strategy in the limit, as the length of each period decreases to zero. We show that the limit optimal strategy is myopic for beliefs smaller than the invariant distribution of the underlying Markov process. For beliefs larger than the invariant distribution, the optimal policy is more elaborate and involves both silence and splitting of the receiver's beliefs; it is not myopic.Moral hazard in remote teamshttps://zbmath.org/1530.910512024-04-15T15:10:58.286558Z"Bisetti, Emilio"https://zbmath.org/authors/?q=ai:bisetti.emilio"Tengelsen, Benjamin"https://zbmath.org/authors/?q=ai:tengelsen.benjamin"Zetlin-Jones, Ariel"https://zbmath.org/authors/?q=ai:zetlin-jones.arielSummary: We reexamine the ability of teams to credibly self-impose group punishments and prevent free riding when individual inputs are unobservable. We formulate self-imposed group punishments as performance underreporting by the team. Although underreporting is not credible in a static game, we show that simple strategies can sustain underreporting in a repeated game, and that the threat of underreporting improves welfare only if team members' preferences between shirking and team output consumption are nonseparable. Our results suggest that self-assessments can replace increased managerial monitoring in remote work environments.
{{\copyright} 2022 The Authors. \textit{International Economic Review} published by Wiley Periodicals LLC on behalf of the Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.}The folk theorem for the prisoner's dilemma with endogenous private monitoringhttps://zbmath.org/1530.910522024-04-15T15:10:58.286558Z"Carmona, Guilherme"https://zbmath.org/authors/?q=ai:carmona.guilherme"Laohakunakorn, Krittanai"https://zbmath.org/authors/?q=ai:laohakunakorn.krittanaiSummary: We study the repeated prisoner's dilemma with private monitoring under the assumption that the monitoring structure is endogenously chosen by the players in each period. We allow the players to choose from all possible monitoring structures. If the players disagree on the monitoring structure they would like, the realized monitoring structure is determined by a function that aggregates their choices. When one player can dictate the monitoring structure, then the repetition of the stage Nash is the only sequential equilibrium outcome. In contrast, when no player can dictate the monitoring structure, we provide conditions on the aggregation function under which any strictly individually rational and feasible payoff vector can be supported in sequential equilibrium.A complete characterization of infinitely repeated two-player games having computable strategies with no computable best response under limit-of-means payoffhttps://zbmath.org/1530.910532024-04-15T15:10:58.286558Z"Dargaj, Jakub"https://zbmath.org/authors/?q=ai:dargaj.jakub"Simonsen, Jakob Grue"https://zbmath.org/authors/?q=ai:simonsen.jakob-grueSummary: It is well-known that for infinitely repeated games, there are computable strategies that have best responses, but no computable best responses. These results were originally proved for either specific games (e.g., prisoner's dilemma), or for classes of games satisfying certain conditions not known to be both necessary and sufficient.
We derive a complete characterization in the form of simple necessary and sufficient conditions for the existence of a computable strategy without a computable best response under limit-of-means payoff. We further refine the characterization by requiring the strategy profiles to be Nash equilibria or subgame-perfect equilibria, and we show how the characterizations entail that it is efficiently decidable whether an infinitely repeated game has a computable strategy without a computable best response.Accomplice plea bargains in the presence of costly juror efforthttps://zbmath.org/1530.910542024-04-15T15:10:58.286558Z"Guha, Brishti"https://zbmath.org/authors/?q=ai:guha.brishtiSummary: This is the first paper to study accomplice plea bargains when motivated jurors incur an effort cost. I find that a prosecutor who wishes to ensure punishment for the guilty, and acquittal for the innocent, induces a unique perfect Bayesian equilibrium which is fully separating, simultaneously minimizing court costs as well as jurors' cognitive efforts. In this equilibrium, a very harsh plea bargain (with negligible plea discounting) is offered, and is accepted by all guilty defendants, and rejected by all innocent ones. Though the prosecutor has the ability to induce semi-separating equilibria, he will prefer the fully separating one. We can use the Cho-Kreps intuitive criterion to show that a pooling equilibrium does not exist. My results contrast sharply with the plea bargaining literature which finds a tradeoff between sorting efficiency and the harshness of punishments meted out to the guilty and which does not support a fully separating equilibrium.The optimal way to play the most difficult repeated two-player coordination gameshttps://zbmath.org/1530.910552024-04-15T15:10:58.286558Z"Kuusisto, Antti"https://zbmath.org/authors/?q=ai:kuusisto.antti"Rönnholm, Raine"https://zbmath.org/authors/?q=ai:ronnholm.raineSummary: This paper investigates repeated win-lose coordination games (\(\mathsf{WLC}\)-games). We analyze which protocols are optimal for these games, covering both the worst case and average case scenarios, i,e., optimizing the guaranteed and expected coordination times. We begin by analyzing choice matching games (\(\mathsf{CM}\)-games) which are a simple yet fundamental type of \(\mathsf{WLC}\)-games, where the goal of the players is to pick the same choice from a finite set of initially indistinguishable choices. We give a fully complete classification of optimal expected and guaranteed coordination times in two-player \(\mathsf{CM}\)-games and show that the corresponding optimal protocols are unique in every case -- except in the \(\mathsf{CM}\)-game with four choices, which we analyze separately.
Our results on \(\mathsf{CM}\)-games are essential for proving a more general result on the difficulty of all \(\mathsf{WLC}\)-games: we provide a complete analysis of least upper bounds for optimal expected coordination times in all two-player \(\mathsf{WLC}\)-games as a function of game size. We also show that \(\mathsf{CM}\)-games can be seen as the most difficult games among all two-player \(\mathsf{WLC}\)-games, as they turn out to have the greatest optimal expected coordination times.Order independence for rationalizabilityhttps://zbmath.org/1530.910562024-04-15T15:10:58.286558Z"Manili, Julien"https://zbmath.org/authors/?q=ai:manili.julienSummary: This paper provides a sufficient monotonicity condition for the solution of a rationalizability procedure to be independent of the order of elimination. The analysis unfolds in an abstract environment that applies to any game and elimination procedure. Monotonicity is satisfied by rationalizability procedures based on monotone belief operators, such as ``directed'' rationalizability, interim correlated rationalizability, or, in sequential games, initial and backwards rationalizability.Cooperative teaching and learning of actionshttps://zbmath.org/1530.910572024-04-15T15:10:58.286558Z"Song, Yangbo"https://zbmath.org/authors/?q=ai:song.yangbo"Zhao, Mofei"https://zbmath.org/authors/?q=ai:zhao.mofeiSummary: This paper studies a novel game-theoretic setting: players may acquire new actions over time by observing the opponent's play. We model this scenario as finitely repeated games where players' action sets are private information and may endogenously expand over time. Three main implications emerge from this framework and its equilibria. First, players may target a payoff vector for the long run and voluntarily ``teach'' one another the actions needed in early periods. The action profile will be learned and sustained as long as each action is available to either player. Second, when no payoff target is prefixed, the players can always obtain or approximate strict ex-post efficiency via bilateral teaching and learning. Third, an alternative economic argument now exists for seemingly irrational cooperative behavior in games with finite horizon. For instance, fully rational players can play a cooperative equilibrium even if the stage game remains a prisoner's dilemma for everyone.Evolution and the ultimatum gamehttps://zbmath.org/1530.910582024-04-15T15:10:58.286558Z"Akdeniz, Aslıhan"https://zbmath.org/authors/?q=ai:akdeniz.aslihan"van Veelen, Matthijs"https://zbmath.org/authors/?q=ai:van-veelen.matthijsSummary: In this paper we review, upgrade, and synthesize existing models from evolutionary game theory, all of which aim at explaining human behaviour in the ultimatum game. Our new and improved versions of \textit{J. Gale} et al. [Games Econ. Behav. 8, No. 1, 56--90 (1995; Zbl 0827.90146)], \textit{M. A. Nowak} et al. [Science 289, No. 5485, 1773--1775 (2000; \url{doi:10.1126/science.289.5485.1773})], and \textit{D. G. Rand} et al. [Proc. Natl. Acad. Sci. USA 110, No. 7, 2581--2586 (2013; Zbl 1292.91050)] avoid shortcomings that the original versions have, one of which is that the results in the first and the last are driven by bias in the mutations. We also compare the predictions of these three models with the existing experimental evidence by looking at properties of the distributions of minimal acceptable offers. We find that the observed distributions do not conform to the predictions from \textit{J. Gale} et al. [Games Econ. Behav. 8, No. 1, 56--90 (1995; Zbl 0827.90146)], \textit{D. G. Rand} et al. [Proc. Natl. Acad. Sci. USA 110, No. 7, 2581--2586 (2013; Zbl 1292.91050)], or any other model in which there is no fitness benefit to rejecting. This does not rule out commitment-based explanations, such as \textit{M. A. Nowak} et al. [Science 289, No. 5485, 1773--1775 (2000; \url{doi:10.1126/science.289.5485.1773})].Sampling dynamics applied to the traveler's dilemma reveals non-Nash behaviorhttps://zbmath.org/1530.910592024-04-15T15:10:58.286558Z"Berkemer, Rainer"https://zbmath.org/authors/?q=ai:berkemer.rainer"Starke, Jens"https://zbmath.org/authors/?q=ai:starke.jens"Kawamoto, Atsushi"https://zbmath.org/authors/?q=ai:kawamoto.atsushi.1Summary: The traveler's dilemma is characterized by a strict Nash equilibrium that is Pareto-inefficient. Even though a coordinated choice of more efficient options would be preferred by both players, any individual deviation from Nash behavior will induce a lower payoff. Yet experimental behavior reported in the literature demonstrates that deviations from Nash behavior toward Pareto-better outcomes are typical. An application of the sampling dynamics to this dilemma further justifies the non-Nash behavior. Due to the fact, that the sampling dynamics is not payoff-monotonic, even dominated strategies can survive the selection process. It is shown that for a generalized traveler's dilemma an interior equilibrium attracts almost all trajectories, given that there are sufficiently many options. The limit for infinitely many options is derived.Similarity suppresses cyclicity: why similar competitors form hierarchieshttps://zbmath.org/1530.910602024-04-15T15:10:58.286558Z"Cebra, Christopher"https://zbmath.org/authors/?q=ai:cebra.christopher"Strang, Alexander"https://zbmath.org/authors/?q=ai:strang.alexanderSummary: Competitive systems can exhibit both hierarchical (transitive) and cyclic (intransitive) structures. Despite theoretical interest in cyclic competition, which offers richer dynamics and occupies a larger subset of the scope of possible competitive systems, most real-world systems are predominantly transitive. Why? Here, we introduce a generic mechanism that promotes transitivity, even when there is ample room for cyclicity. We demonstrate that, if competitive outcomes depend smoothly on competitor attributes, then similar competitors compete transitively. We quantify the rate of convergence to transitivity given the similarity of the competitors and the smoothness of the performance function. Thus, we prove the adage regarding apples and oranges. Similar objects admit well-ordered comparisons; diverse objects may not.Stochastic replicator dynamics: a theoretical analysis and an experimental assessmenthttps://zbmath.org/1530.910612024-04-15T15:10:58.286558Z"Choudhury, Kangkan Dev"https://zbmath.org/authors/?q=ai:choudhury.kangkan-dev"Aydinyan, Tigran"https://zbmath.org/authors/?q=ai:aydinyan.tigranSummary: We study the dynamics of strategic choice in an environment where payoffs are perturbed by strategy-specific noise and strategy revision is governed by the simple proportional imitation protocol. Applying the stochastic replicator dynamic to a two-by-two symmetric game, we derive the steady-state frequencies of the strategies and show that the dominated strategy can persist in equilibrium if the variance of the payoff shocks exceeds a critical value. Additionally, the rate of decay of the dominated strategy decreases with increasing variance. The behaviours of our experimental subjects accord with these tendencies. Our findings add to the growing experimental literature that demonstrates that evolutionary models of human behaviour with simple adaptive rules have predictive ability, even in complex, volatile environments.Stable and historic behavior in replicator equations given by nonlinear mappingshttps://zbmath.org/1530.910622024-04-15T15:10:58.286558Z"Saburov, Mansoor"https://zbmath.org/authors/?q=ai:saburov.mansoor|saburov.mansur-kh(no abstract)Evolutionary dynamics in heterogeneous populations: a general framework for an arbitrary type distributionhttps://zbmath.org/1530.910632024-04-15T15:10:58.286558Z"Zusai, Dai"https://zbmath.org/authors/?q=ai:zusai.daiSummary: We present a general framework of evolutionary dynamics under persistent heterogeneity in payoff functions and revision protocols, allowing continuously many types in a game with finitely many strategies. Unlike existing literature, we do not assume anonymity of the game nor aggregability of the dynamic. The dynamic is formulated as a differential equation of a joint probability measure of types and strategies. To establish a foundation for this framework, we clarify regularity assumptions on the revision protocol, the game, and the type distribution to guarantee the existence of a unique solution trajectory as well as those to guarantee the existence of an equilibrium in a heterogeneous population game. We further verify equilibrium stationarity in general and stability in potential games under admissible dynamics. Our framework encompasses a wide range of possible applications, including incomplete information games and spatial evolution.Differential games for crowd dynamics and applicationshttps://zbmath.org/1530.910642024-04-15T15:10:58.286558Z"Barreiro-Gomez, Julian"https://zbmath.org/authors/?q=ai:barreiro-gomez.julian"Masmoudi, Nader"https://zbmath.org/authors/?q=ai:masmoudi.naderSummary: We study crowd dynamics by means of both non-atomic and atomic differential games, which are also known as macroscopic and microscopic models, respectively; and we consider few crowd-related applications and experiments. Mainly, we study the modeling for Hajj motion (Tawaf), the most important event for Muslim pilgrims taking place in Mecca. We formally show that the proposed game-theoretical model is a potential-cost-dependent version of the well-known Hughes model, and the existing connection with the Lighthill-Whitham-Richards traffic model. We show that for a particular value in the potential cost, one obtains the same Hughes crowd model. Hence, we introduce a mild approximation that allows the computation of semi-explicit/explicit solutions for the proposed game problems. We study four main components that may be used by a central planner: (i) the effect of the clusters (delegations) over the motion, (ii) the inflow control to optimize the flux, (iii) how organized crowds evolve in comparison to disorganized ones, and (iv) how the creation of corrals with time-delays over their motion can be beneficial for the crowd evolution efficiency. We show that a faster performance is exhibited when pilgrims do Tawaf individually than when clustered groups are made, suggesting a possible direction for the policies design. Hence, we also present a simple ON/OFF control over the inflow that can be implemented by a central planner such that the flux is maximized. Related to this last mentioned policy, we have shown that delaying a group to integrate into the crowd can be beneficial for their efficient and faster motion. Also, we show that organized crowds evolve faster than disorganized ones, suggesting that education programs to perform Tawaf may potentially improve the flow. Finally, we show that other type of behaviors could be captured by means of the appropriate design of the cost functional. For example, the consideration of stress during an evacuation can be captured by means of the suitable modification of the cost functional, and as another example, we model the drafting tactics in bicycling where small densities can be beneficial for the performance. We present numerical and simulation results for all the applications using both the macroscopic and microscopic models, which certify the suitability of these models to capture the main features of the real behavior.A modified method of resolving functions for game control problems with integral constraintshttps://zbmath.org/1530.910652024-04-15T15:10:58.286558Z"Chikrii, A. A."https://zbmath.org/authors/?q=ai:chikrii.arkadii-a"Rappoport, I. S."https://zbmath.org/authors/?q=ai:rappoport.i-sSummary: The authors consider linear differential games with integral constraints. Sufficient conditions for the game termination in a finite guaranteed time are formulated for the case where the Nikolsky condition is not satisfied. Multivalued mappings that generate the upper and lower resolving functions of special type are introduced. The modified schemes of the Nikolsky direct method and the method of resolving functions are proposed, which ensure the game termination in a finite guaranteed time in the class of quasi-strategies and stroboscopic strategies. The most recent theoretical results are illustrated by the reference Pontryagin's example with objects of the same type.Control of moving objects in condition of conflicthttps://zbmath.org/1530.910662024-04-15T15:10:58.286558Z"Chikrii, Arkadii A."https://zbmath.org/authors/?q=ai:chikrii.arkadii-aFor the entire collection see [Zbl 1522.93012].Non-autonomous linear quadratic non-cooperative differential games with continuous updatinghttps://zbmath.org/1530.910672024-04-15T15:10:58.286558Z"Kuchkarov, Ildus"https://zbmath.org/authors/?q=ai:kuchkarov.ildus-i"Petrosian, Ovanes"https://zbmath.org/authors/?q=ai:petrosyan.ovanes-l"Li, Yin"https://zbmath.org/authors/?q=ai:li.yin.1Summary: The subject of this paper is a non-autonomous linear quadratic case of a differential game model with continuous updating. This class of differential games is essentially new where it is assumed that, at each time instant, players have or use information about the game structure defined on a closed time interval with a fixed duration. During the interval information about motion equations and payoff functions of players updates. It is non-autonomy that simulates this effect of updating information. A linear quadratic case for this class of games is particularly important for practical problems arising in the engineering of human-machine interaction. Here we define the Nash equilibrium as an optimality principle and present an explicit form of Nash equilibrium for the linear quadratic case. Also, the case of dynamic updating for the linear quadratic differential game is studied and uniform convergence of Nash equilibrium strategies and corresponding trajectory for a case of continuous updating and dynamic updating is demonstrated.
For the entire collection see [Zbl 1522.91009].A novel cooperative-competitive differential graphical game with distributed global Nash solutionhttps://zbmath.org/1530.910682024-04-15T15:10:58.286558Z"Noorighanavati Zadeh, Hossein"https://zbmath.org/authors/?q=ai:noorighanavati-zadeh.hossein"Afshar, Ahmad"https://zbmath.org/authors/?q=ai:afshar.ahmadSummary: This paper investigates a differential graphical game problem for fixed communication topology networks, where simultaneous mutual cooperative-competitive (CC) effects exist among the agents. The objective of such a system is to design distributed control policies that synchronize agents to a leader's trajectory and achieve a Nash equilibrium. We point out that existing frameworks in multi-agent and game theory fields do not explicitly define and formulate co-existed CC effects between agents. To fill this gap, we propose a novel differential graphical game named \textit{cooperative-competitive differential graphical game (CCDGG),} where such effects are modeled for each agent by introducing a new parameter called ``collective cooperative-competitive impact factor (CCCIF)''. It is shown that the performance indices proposed in the literature cannot provide a distributed solution to the CCDGG. We propose novel performance indices which generate decoupled Hamilton-Jacobi (HJ) equations when agents use the best response strategy. This will consequently lead to a distributed Nash solution for CCDGG. The closed-loop stability and Nash equilibrium properties for CCDGG are also analyzed and proved. Finally, derived theoretical results are validated through numerical simulations.Cops and robber on butterflies, grids, and AT-free graphshttps://zbmath.org/1530.910692024-04-15T15:10:58.286558Z"Akhtar, Sheikh Shakil"https://zbmath.org/authors/?q=ai:akhtar.sheikh-shakil"Das, Sandip"https://zbmath.org/authors/?q=ai:das.sandip"Gahlawat, Harmender"https://zbmath.org/authors/?q=ai:gahlawat.harmenderSummary: \textsc{Cops and Robber} is a well-studied two player pursuit-evasion game played on a graph. In this game, a set of cops, controlled by the first player, tries to capture the position of a robber, controlled by the second player. The \textit{cop number} of a graph is the minimum number of cops required to capture the robber in the graph. A group of cops \textit{guard} a subgraph if they can ensure that the robber cannot enter the subgraph without getting captured immediately.
We study the applications of guarding to provide new bounds and improve existing bounds for several graph classes. In particular, we show that the cop number for butterfly networks and for solid grids is two. We also construct a partial grid with cop number 3 establishing that partial grids have same cop number as their superclass planar graphs. We also consider three well-studied variants of \textsc{Cops and Robber : Cops and Fast Robber, Cops and Attacking Robber}, and \textsc{Surrounding CnR}. We improve the existing bounds for the cop number of multidimensional grids for both \textsc{Cops and Attacking Robber} and \textsc{Surrounding CnR}. Finally, we consider \textsc{Cops and Fast Robber} on AT-free graphs to improve the existing bounds on the cop number for this game.On game problems of controlling pencil trajectories under integral constraints on the controls of playershttps://zbmath.org/1530.910702024-04-15T15:10:58.286558Z"Mamadaliev, N. A."https://zbmath.org/authors/?q=ai:mamadaliev.numanzhon-alimdzhanovich"Ibaydullaev, T. T."https://zbmath.org/authors/?q=ai:ibaydullaev.t-t"Abdualimova, G. M."https://zbmath.org/authors/?q=ai:abdualimova.gulzurakhon-mirzakomilovnaSummary: The game problems of control of pencil trajectories, described by a system of equations with a retarded argument under integral restrictions on the players' controls, are studied. Modifications of the first (I) and third (III) pursuit methods are proposed for game problems of control pencil trajectories. For this game, sufficient conditions are obtained for the possibility of transferring pencil trajectories.Direct method for solving game problems of approach of controlled objectshttps://zbmath.org/1530.910712024-04-15T15:10:58.286558Z"Chikrii, A. A."https://zbmath.org/authors/?q=ai:chikrii.arkadii-a"Rappoport, I. S."https://zbmath.org/authors/?q=ai:rappoport.i-sSummary: The authors analyze the problem of approach of controlled objects in dynamic game problems. The sufficient conditions for the game termination in a finite guaranteed time are obtained when the classical Pontryagin condition is not satisfied. Instead of the Pontryagin selection, which does not exist, some shift function is considered. With its help, a special set-valued mapping is introduced, which generates a lower resolving function. The latter plays a key role in formulating the result and allows constructing the control based on theorems of the Filippov-Castaing kind. A modified scheme of Pontryagin's first direct method is proposed, which ensures a successful completion of the conflict-controlled process in the class of counter-controls. To compare the guaranteed times, the upper resolving function is introduced, and the corresponding scheme of the method is provided. The theoretical results are illustrated with a model example.Dynamic games with incomplete knowledge in metric spaceshttps://zbmath.org/1530.910722024-04-15T15:10:58.286558Z"Konnov, Igor"https://zbmath.org/authors/?q=ai:konnov.igor-vSummary: We describe a model of a discrete time dynamic system with active elements (players) and states in a metric space. Each state is associated with the common utility value and player shares. Coalitions of players can change the system state, but each move requires their expenses. The players may have only restricted and local knowledge about the system. We define the concept of an equilibrium state in this dynamic game and present iterative algorithms that create feasible trajectories tending to equilibrium states under rather general conditions.
For the entire collection see [Zbl 1522.91009].Irreversibility and monitoring in dynamic games: experimental evidencehttps://zbmath.org/1530.910732024-04-15T15:10:58.286558Z"Lee, Eungik"https://zbmath.org/authors/?q=ai:lee.eungik"Choi, Andrew"https://zbmath.org/authors/?q=ai:choi.andrew"Choi, Syngjoo"https://zbmath.org/authors/?q=ai:choi.syngjoo"Guéron, Yves"https://zbmath.org/authors/?q=ai:gueron.yvesSummary: This article provides experimental evidence on the impacts of irreversibility and imperfect monitoring on the efficiency and the equity of a repeated public goods game. We find that irreversibility and imperfect monitoring both lead to inefficient and unequal outcomes through different channels. Irreversibility lowers public goods contribution in earlier periods and makes the initial-period contribution gap between two players long-lasting. Imperfect monitoring hampers conditional cooperation and persistently reduces group contribution. A finite mixture estimation with conditional cooperators provides a coherent account of the treatment effects.
{{\copyright} 2022 the Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.}Empowering of candidates and parties in single term vs re-election schemeshttps://zbmath.org/1530.910742024-04-15T15:10:58.286558Z"López, Fernanda Herrera"https://zbmath.org/authors/?q=ai:lopez.fernanda-herrera"Cantala, David"https://zbmath.org/authors/?q=ai:cantala.davidSummary: Agenda setting is a key feature of political systems. We propose a novel approach to contrast the respective power of candidates and parties when bargaining over agenda, which consists in comparing the simulations of four institutional models: single term with candidates proposing, single term with parties proposing, two-term with candidates proposing and two-term with parties proposing. Valences of candidates and preferences for alternation of voters are two important components of the analysis. Simulations establish that two-term schemes are inefficient, while term limits is a second order component of the agenda setting bargaining, while the offering side is the main component.Estimation of (static or dynamic) games under equilibrium multiplicityhttps://zbmath.org/1530.910752024-04-15T15:10:58.286558Z"Otsu, Taisuke"https://zbmath.org/authors/?q=ai:otsu.taisuke"Pesendorfer, Martin"https://zbmath.org/authors/?q=ai:pesendorfer.martin"Sasaki, Yuya"https://zbmath.org/authors/?q=ai:sasaki.yuya"Takahashi, Yuya"https://zbmath.org/authors/?q=ai:takahashi.yuyaSummary: We propose a multiplicity-robust estimation method for static or dynamic games. The method allows for distinct behaviors and strategies across markets by treating market-specific behaviors as correlated latent variables, with their conditional probability measure treated as an infinite-dimensional nuisance parameter. Instead of solving the intermediate infinite-dimensional optimization problem, we consider the equivalent finite-dimensional dual problem. This property allows for a practically feasible characterization of the identified region for the structural parameters. We apply the estimation method to newspaper market previously studied in [\textit{M. J. Gentzkow} et al., ``Competition and Ideological Diversity: Historical Evidence from US Newspapers'', American Economic Review, 104, 3073--3114 (2014)] to characterize the identified region of marginal costs.
{{\copyright} (2021) by the Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.}Owen value for dynamic games on networks91A43https://zbmath.org/1530.910762024-04-15T15:10:58.286558Z"Petrosyan, Leon"https://zbmath.org/authors/?q=ai:petrosyan.leon-aganesovich"Pankratova, Yaroslavna B."https://zbmath.org/authors/?q=ai:pankratova.yaroslavna-bSummary: In the presented paper, we consider dynamic network games with coalition structure in which players cooperate to get the best outcomes. As solution the Owen value is proposed. To simplify the calculations the new characteristic function is introduced based on the possibility of cutting connections by players outside the coalition. For a special case, comparison of the Owen value with other solutions is done.
For the entire collection see [Zbl 1522.91009].On durable-strategies dynamic game theoryhttps://zbmath.org/1530.910772024-04-15T15:10:58.286558Z"Yeung, David W. K."https://zbmath.org/authors/?q=ai:yeung.david-wing-kay"Zhang, Yingxuan"https://zbmath.org/authors/?q=ai:zhang.yingxuanSummary: An empirically meaningful theory of dynamic games has to incorporate real-life phenomena. Durable strategies, which effects last for a period of time, are prevalent in real-life situations. Revenue generating investments, toxic waste disposal and purchase of durable goods are common examples of durable strategies. This paper first provides a review on durable-strategies dynamic game theory. A practically relevant advancement -- random horizon durable-strategies dynamic games -- yielding novel results in durable-strategies dynamic games theory is then presented. Dynamic optimization theorem, game formulations and HJB equations are derived. An illustrative example is provided. The theory and solution mechanism of durable-strategies cooperative dynamic games are also discussed.
For the entire collection see [Zbl 1522.91009].A multi-agent model of misspecified learning with overconfidencehttps://zbmath.org/1530.910782024-04-15T15:10:58.286558Z"Ba, Cuimin"https://zbmath.org/authors/?q=ai:ba.cuimin"Gindin, Alice"https://zbmath.org/authors/?q=ai:gindin.aliceSummary: This paper studies the long-term interaction between two overconfident agents who choose how much effort to exert while learning about their environment. Overconfidence causes agents to underestimate either a common fundamental, such as the underlying quality of their project, or their counterpart's ability, to justify their worse-than-expected performance. We show that in many settings, agents create informational externalities for each other. When informational externalities are positive, the agents' learning processes are mutually-reinforcing: one agent best responding to his own overconfidence causes the other agent to reach a more distorted belief and take more extreme actions, generating a positive feedback loop. The opposite pattern, mutually-limiting learning, arises when informational externalities are negative. We also show that in our multi-agent environment, overconfidence can lead to Pareto improvement in welfare. Finally, we prove that under certain conditions, agents' beliefs and effort choices converge to a steady state that is a Berk-Nash equilibrium.Cautious belief and iterated admissibilityhttps://zbmath.org/1530.910792024-04-15T15:10:58.286558Z"Catonini, Emiliano"https://zbmath.org/authors/?q=ai:catonini.emiliano"De Vito, Nicodemo"https://zbmath.org/authors/?q=ai:de-vito.nicodemoSummary: We define notions of cautiousness and cautious belief to provide epistemic conditions for iterated admissibility in finite games. We show that iterated admissibility characterizes the behavioral implications of ``cautious rationality and common cautious belief in cautious rationality'' in a terminal lexicographic type structure. For arbitrary type structures, the behavioral implications of these epistemic assumptions are characterized by the solution concept of self-admissible set
[\textit{A. Brandenburger} et al., Econometrica 76, No. 2, 307--352 (2008; Zbl 1133.91330)].
We also show that analogous results hold under alternative epistemic assumptions, in particular if cautiousness is ``transparent'' to the players.Iterated bounded dominancehttps://zbmath.org/1530.910802024-04-15T15:10:58.286558Z"Hsieh, Yue-Da"https://zbmath.org/authors/?q=ai:hsieh.yue-da"Qian, Xuewen"https://zbmath.org/authors/?q=ai:qian.xuewen"Qu, Chen"https://zbmath.org/authors/?q=ai:qu.chenSummary: Motivated by the desideratum of undominated dominators [\textit{M. O. Jackson}, Rev. Econ. Stud. 59, No. 4, 757--775 (1992; Zbl 0771.90004)], we provide a notion of iterated elimination of boundedly dominated strategies for (in)finite strategic games and a wide variety of dominance relations. By introducing a condition of forgetfulness-proofness, we establish the equivalence among the usual iterated dominance, our notion of iterated bounded dominance, and Gilboa, Kalai and Zemel's procedure [\textit{I. Gilboa} et al., Oper. Res. Lett. 9, No. 2, 85--89 (1990; Zbl 0696.90091)]. We also investigate the connection of forgetfulness-proofness with other similar conditions in the literature.Common assumption of rationalityhttps://zbmath.org/1530.910812024-04-15T15:10:58.286558Z"Keisler, H. Jerome"https://zbmath.org/authors/?q=ai:keisler.h-jerome"Lee, Byung Soo"https://zbmath.org/authors/?q=ai:lee.byung-sooSummary: We build on the work of
\textit{A. Brandenburger} et al. [Econometrica 76, No. 2, 307--352 (2008; Zbl 1133.91330)] (BFK)
by showing that \textit{rationality and common assumption of rationality (RCAR)} is possible in complete lexicographic type structures and characterizes iterated admissibility -- i.e., iterated elimination of weakly dominated strategies. Our result is unexpected in light of
BFK's
result proving the impossibility of RCAR in continuous complete lexicographic type structures. We reconcile the two by showing that continuous complete lexicographic type structures differ from complete lexicographic type structures that admit RCAR only in how much caution -- in a sense that we formalize -- is required to assume events.Behavioral implementation under incomplete informationhttps://zbmath.org/1530.910822024-04-15T15:10:58.286558Z"Barlo, Mehmet"https://zbmath.org/authors/?q=ai:barlo.mehmet"Dalkıran, Nuh Aygün"https://zbmath.org/authors/?q=ai:dalkiran.nuh-aygunSummary: We investigate implementation under incomplete information allowing for individuals' choices featuring violations of rationality. Our primitives are individuals' interim choices that do not have to satisfy the weak axiom of revealed preferences. In this setting, we provide necessary as well as sufficient conditions for behavioral implementation under incomplete information. We also introduce behavioral interim incentive Pareto efficiency and investigate its implementability under incomplete information.Setting an exam as an information design problemhttps://zbmath.org/1530.910832024-04-15T15:10:58.286558Z"Shimoji, Makoto"https://zbmath.org/authors/?q=ai:shimoji.makotoSummary: We take a teacher's exam-setting task as an information design problem. Specifically, the teacher chooses a conditional distribution of grades given students' types. After observing their exam results, each student updates her belief regarding her type via Bayes' rule and chooses an action. Students' reactions to the same exam result could be different, depending on their heterogeneous prior beliefs. The teacher's objective is to persuade students to take a certain action (e.g., applying to universities), which some may not choose without an exam. The teacher adopts different grade distributions, depending on the teacher's and the students' heterogeneous prior beliefs.
{\copyright} 2022 The Authors. \textit{International Journal of Economic Theory} published by John Wiley \& Sons Australia, Ltd on behalf of International Association for Economic Theory.Independent versus collective expertisehttps://zbmath.org/1530.910842024-04-15T15:10:58.286558Z"Catonini, Emiliano"https://zbmath.org/authors/?q=ai:catonini.emiliano"Kurbatov, Andrey"https://zbmath.org/authors/?q=ai:kurbatov.andrey"Stepanov, Sergey"https://zbmath.org/authors/?q=ai:stepanov.sergey-n|stepanov.sergei-pavlovich|stepanov.sergey-s|stepanov.sergey-y|stepanov.sergey-eSummary: We consider the problem of a decision-maker who seeks for advice from several experts. The experts have reputation concerns which generate incentives to herd on the prior belief about the state of the world. We address the following question: Should the experts be allowed to exchange their information before providing advice (``collective expertise'') or not (``independent expertise'')? We show that collective expertise is more informative than independent expertise under low prior uncertainty about the state and less informative otherwise. We also argue that collective expertise gains advantage as the number of experts grows.Communication between unbiased agentshttps://zbmath.org/1530.910852024-04-15T15:10:58.286558Z"Dilmé, Francesc"https://zbmath.org/authors/?q=ai:dilme.francescSummary: We examine a version of the model of \textit{V. P. Crawford} and \textit{J. Sobel} [Econometrica 50, 1431--1451 (1982; Zbl 0494.94007)] in which agents are not biased, but their preferences are not necessarily smooth. In this situation, we show that communication converges to full information transmission as the number of messages used for communication increases if and only if the sender and the receiver have the same local relative preferences for avoiding small ``upward'' or ``downward'' mistakes. When these conditions fail, either an arbitrarily small bias or an arbitrarily small noise in the observation of the state may make communication very coarse in all equilibria, even when the message space is infinite. Hence, contrary to what was previously thought, continuity of preferences and close alignment between the sender's and receiver's ideal actions do not guarantee the existence of equilibria with precise information transmission.Strategic transmission of imperfect information: why revealing evidence (without proof) is difficulthttps://zbmath.org/1530.910862024-04-15T15:10:58.286558Z"Foerster, Manuel"https://zbmath.org/authors/?q=ai:foerster.manuelSummary: In our cheap-talk setting, an expert privately observes multiple binary signals, her soft evidence, about a continuous state of the world and then communicates with a decision-maker. While direct transmission of evidence entails communicating the underlying signals, indirect transmission of evidence entails communicating a summary statistic of her evidence. We first establish that fully informative equilibria exist if the conflict of interest is small. Otherwise, direct transmission of evidence is impossible, as withholding one part of the soft evidence in the communication necessarily induces incentives to manipulate the report on the other part. On the contrary, indirect transmission of evidence remains partially informative for intermediate conflicts of interest. Finally, we introduce the possibility of certification. We show that, if the costs of certification are low, the expert can fully reveal her evidence regardless of the conflict of interest.Information revelation and coordination using cheap talk in a game with two-sided private informationhttps://zbmath.org/1530.910872024-04-15T15:10:58.286558Z"Ganguly, Chirantan"https://zbmath.org/authors/?q=ai:ganguly.chirantan"Ray, Indrajit"https://zbmath.org/authors/?q=ai:ray.indrajitSummary: We consider a version of the Battle of the Sexes with private information and allow cheap talk regarding the players' types before the game. We show that a desirable type-coordination property is achieved at the unique fully revealing symmetric equilibrium (when it exists). Type-coordination is also obtained in a partially revealing equilibrium that exists when the fully revealing equilibrium does not. We further prove that truthfully revealed messages, followed by actions that depend meaningfully on these messages, are not equilibrium profiles with one-sided cheap talk. Finally, fully revealing equilibria do not exist under sequential communication either.Court-appointed experts and accuracy in adversarial litigationhttps://zbmath.org/1530.910882024-04-15T15:10:58.286558Z"Kim, Chulyoung"https://zbmath.org/authors/?q=ai:kim.chulyoung"Koh, Paul S."https://zbmath.org/authors/?q=ai:koh.paul-sSummary: Concerned about distortion of evidence arising from litigants' strong incentive to misrepresent information provided to fact-finders, legal scholars and commentators have long suggested that courts appoint their own advisors for neutral information regarding disputes. This paper examines the litigants' problem of losing incentive to provide information when judges seek the advice of court-appointed experts. Within a standard litigation-game framework, we find that assigning court-appointed experts involves a trade-off: although such experts help judges obtain more information overall, thereby reducing the number of errors during trials, they weaken litigants' incentive to supply expert information, thus undermining the adversarial nature of the current American legal system.
{{\copyright} IAET}Linear Riley equilibria in quadratic signaling gameshttps://zbmath.org/1530.910892024-04-15T15:10:58.286558Z"Weng, Xi"https://zbmath.org/authors/?q=ai:weng.xi"Wu, Fan"https://zbmath.org/authors/?q=ai:wu.fan"Yin, Xundong"https://zbmath.org/authors/?q=ai:yin.xundongSummary: We study signaling games with quadratic payoffs. As signaling games admit multiple separating equilibria, many equilibrium selection rules are proposed and a well-known solution is Riley equilibria. They are separating equilibria in which the sender achieves the highest equilibrium payoff for all types among all separating equilibria. We analyze the conditions for Riley equilibria to be linear, a common assumption in many applications. We derive a sufficient and necessary condition for the existence and uniqueness of linear Riley equilibria. We apply the result to confirm the dominance of linear equilibria in some classic examples, and we show that, in some other examples, there exist previously unknown nonlinear Riley equilibria.Morphisms of open gameshttps://zbmath.org/1530.910902024-04-15T15:10:58.286558Z"Hedges, Jules"https://zbmath.org/authors/?q=ai:hedges.julesSummary: We define a notion of morphisms between open games, exploiting a surprising connection between lenses in computer science and compositional game theory. This extends the (perhaps more intuitively obvious) definition of globular morphisms as mappings between strategy profiles that preserve best responses, and hence in particular preserve Nash equilibria. We construct a symmetric monoidal double category in which the horizontal 1-cells are open games, vertical 1-morphisms are lenses, and 2-cells are morphisms of open games. States (morphisms out of the monoidal unit game) in the vertical category give a flexible solution concept that includes both Nash and subgame perfect equilibria. Products in the vertical category give an external choice operator that is reminiscent of products in game semantics, and is useful in practical examples. We illustrate the above two features with a simple worked example from microeconomics, the market entry game.
For the entire collection see [Zbl 1411.68020].Best-response equilibrium: an equilibrium in finitely additive mixed strategieshttps://zbmath.org/1530.910912024-04-15T15:10:58.286558Z"Milchtaich, Igal"https://zbmath.org/authors/?q=ai:milchtaich.igalSummary: A generalization of mixed strategy equilibrium is proposed, where mixed strategies need only be finitely additive and payoff functions are not required to be integrable or bounded. This notion of best-response equilibrium is based on an extension of the idea that an equilibrium strategy is supported in the player's set of best-response actions, but is applicable also when no best-response actions exist. It yields simple, natural equilibria in a number of well-known games where other kinds of mixed equilibrium are complicated, not compelling or do not exist.Game theoretic approach to multi-agent transportation problems on networkhttps://zbmath.org/1530.910922024-04-15T15:10:58.286558Z"Alkhaled, Khaled"https://zbmath.org/authors/?q=ai:alkhaled.khaled"Petrosyan, Leon"https://zbmath.org/authors/?q=ai:petrosyan.leon-aganesovichSummary: In this paper, we consider a network game where players are multi-agent systems (we call them in this paper ``coalitions'') under the condition that the trajectories of players (coalitions) should (have no common arcs, or have no common vertices) i.e., must not intersect. In the same time the trajectories of players inside coalition can intersect (have common arcs,or have common vertices). The last condition complicates the problem, since the sets of strategies turn out to be mutually dependent. A family of Nash equilibrium is constructed and it is also shown that the minimum total time (cost) of players is achieved in a strategy profile that is a Nash equilibrium. A cooperative approach to solving the problem is proposed. Also, another cooperative mini maximal approach to solving the problem is investigated. We also consider the proportional solution and the Shapley value to allocate total minimal costs between players. Two approaches for constructing the characteristic function have been developed.
For the entire collection see [Zbl 1522.91009].Best-response dynamics in directed network gameshttps://zbmath.org/1530.910932024-04-15T15:10:58.286558Z"Bayer, Péter"https://zbmath.org/authors/?q=ai:bayer.peter"Kozics, György"https://zbmath.org/authors/?q=ai:kozics.gyorgy"Szőke, Nóra Gabriella"https://zbmath.org/authors/?q=ai:szoke.nora-gabriellaSummary: We study public goods games played on networks with possibly non-reciprocal relationships between players. These include one-sided relationships, mutual but unequal relationships, and parasitism. It is known that many learning processes converge to the game's Nash equilibrium if interactions are reciprocal, but this is not true in general for directed networks. Under one-sided and parasitic relationships, best-response dynamics may cycle. The production of the locally public good of players may fail to converge to an equilibrium, making static analysis less insightful in an applied setting. In this paper we show that the strong convergence results of the undirected case are retained for two economically relevant classes of directed networks: those with transitive relative importance of players and those rescalable into networks with weak externalities.A model of the formation of multilayer networkshttps://zbmath.org/1530.910942024-04-15T15:10:58.286558Z"Billand, Pascal"https://zbmath.org/authors/?q=ai:billand.pascal"Bravard, Christophe"https://zbmath.org/authors/?q=ai:bravard.christophe"Joshi, Sumit"https://zbmath.org/authors/?q=ai:joshi.sumit"Mahmud, Ahmed Saber"https://zbmath.org/authors/?q=ai:mahmud.ahmed-saber"Sarangi, Sudipta"https://zbmath.org/authors/?q=ai:sarangi.sudiptaSummary: We study the formation of multilayer networks where payoffs are determined by the degrees of players in each network. We begin by imposing either concavity or convexity in degree on the payoff function of the players. We then explore distinct network relationships that result from inter- and intra-network spillovers captured by the properties of supermodularity/submodularity and strategic complementarity respectively. We show the existence of equilibria and characterize them. Additionally, we establish both necessary and sufficient conditions for an equilibrium to occur. We also highlight the connection, in equilibrium, between inter-network externalities and the identity of linked players in one network given the identity of linked players in the other network. Furthermore, we analyze efficient multilayer networks. Finally, we extend our models to contexts with more than two layers, and scenarios where agents receive a bonus for being connected to the same individuals in both networks.Cooperation in the multi-agent system with different types of interactionshttps://zbmath.org/1530.910952024-04-15T15:10:58.286558Z"Grinikh, Aleksandra L."https://zbmath.org/authors/?q=ai:grinikh.aleksandra-lSummary: This paper summarizes the list of our works that contain researches about optimality principles for the ``\(n\)-person prisoner's dilemma'' game. The classic model is considered through the new payoff function for each player that allows to consider it without restrictions for the number of players. The new characteristic function gives an opportunity to introduce the time-consistent subset of the core of the dynamic game. In accordance with this type of game we consider some specific properties of players' payoffs and construct the new way of their interactions. Using the network representation, the classic model is modified to the wider class of games that allows to specify players' influence to each other's payoff function. These investigations can be used for the description of cooperation in the other multi-agent systems.
For the entire collection see [Zbl 1522.91009].Two-stage minimum cost spanning tree game under fuzzy optimistic coalitionhttps://zbmath.org/1530.910962024-04-15T15:10:58.286558Z"Guo, Zhao"https://zbmath.org/authors/?q=ai:guo.zhao"Wang, Dan"https://zbmath.org/authors/?q=ai:wang.dan|wang.dan.1"Chen, Min"https://zbmath.org/authors/?q=ai:chen.min.2|chen.min.1|chen.min.3|chen.min|chen.min.6"Li, Yin"https://zbmath.org/authors/?q=ai:li.yin.1|li.yinSummary: This paper discusses the problem of cost allocation when players have different levels of optimism based on the two-stage minimum spanning tree game, and uses Choquet integral to calculate the characteristic function of fuzzy optimistic coalition and fuzzy pessimistic coalition. It is proved that the subgame of the two-stage clear optimistic coalition minimum cost spanning tree game is also a convex game. Finally, an example is used to prove that the two-stage fuzzy pessimistic coalition minimum cost spanning tree game has a dynamical instability solution.
For the entire collection see [Zbl 1522.91009].The enemy of my enemy is my friend: new conditions for network gameshttps://zbmath.org/1530.910972024-04-15T15:10:58.286558Z"Koizumi, Hideto"https://zbmath.org/authors/?q=ai:koizumi.hidetoSummary: Group formation tends to involve peer effects. In the presence of such complementarities, however, coalitional games need not have a nonempty core. With a restricted preference structure, I provide new sufficient conditions for the nonemptiness of the core of network games that involve pairwise complementarities between peers. The conditions are twofold: (a) sign-consistency -- all agents agree on the sign of the value of any link -- and (b) sign-balance -- the enemy of my enemy is my friend. My conditions provide a game-theoretic explanation for the longevity of the dichotomy of political alliances in the contemporary world.Distributed Nash equilibrium seeking with order-reduced dynamics based on consensus exact penaltyhttps://zbmath.org/1530.910982024-04-15T15:10:58.286558Z"Liang, Shu"https://zbmath.org/authors/?q=ai:liang.shu"Liu, Shuyu"https://zbmath.org/authors/?q=ai:liu.shuyu"Hong, Yiguang"https://zbmath.org/authors/?q=ai:hong.yiguang"Chen, Jie"https://zbmath.org/authors/?q=ai:chen.jie.1(no abstract)Importance of agents in networks: clique based game-theoretic approachhttps://zbmath.org/1530.910992024-04-15T15:10:58.286558Z"Li, Juping"https://zbmath.org/authors/?q=ai:li.juping"Tur, Anna"https://zbmath.org/authors/?q=ai:tur.anna"Zavrajnov, Maksim"https://zbmath.org/authors/?q=ai:zavrajnov.maksimSummary: Centrality measures are commonly used to detect important nodes. There are some metrics that measure a node's connectivity to different communities. This paper extends the standard network centrality measures and proposes to estimate the importance of nodes in network as a solution of a cooperative game. Three ways of defining such cooperative game are introduced. Each of them uses the concept of a clique in graph. Examples are considered.
For the entire collection see [Zbl 1522.91009].Coordination with heterogeneous interaction constraintshttps://zbmath.org/1530.911002024-04-15T15:10:58.286558Z"Lu, Feifei"https://zbmath.org/authors/?q=ai:lu.feifei"Shi, Fei"https://zbmath.org/authors/?q=ai:shi.feiSummary: We study a coevolutionary model of network formation in minimum-effort games. Agents dynamically choose both their effort levels and their interaction partners, but face heterogeneous constraints on how many partners they can interact with. The dynamics under heterogeneity behaves very differently from the one in the homogeneous case, with gradual transitions spreading across the population stepwise instead of sudden adoptions. The long-run outcomes depend crucially on the distribution of interaction constraints. The efficient (highest-effort) convention prevails in the long run even when many agents have loose constraints, if enough agents have tight constraints. The lowest-effort convention dominates if too many agents have loose constraints. The coexistence of conventions is also possible for certain distributions of constraints.A two-stage network interdiction-monitoring gamehttps://zbmath.org/1530.911012024-04-15T15:10:58.286558Z"Nguyen, Di H."https://zbmath.org/authors/?q=ai:nguyen.di-h"Song, Yongjia"https://zbmath.org/authors/?q=ai:song.yongjia"Smith, J. Cole"https://zbmath.org/authors/?q=ai:smith.j-coleSummary: We study a network interdiction problem involving two agents: a defender and an evader. The evader seeks to traverse a path from a source node to a terminus node in a directed network without being detected. The game takes place in two stages. In the first stage, the defender removes a set of arcs in the network. In the second stage, the defender and evader play a simultaneous game. The defender monitors a set of arcs, thus increasing the probability that the evader will be detected on that arc (if the evader uses the arc). The evader selects a source-terminus path. Because the second stage is played simultaneously, both agents use mixed-strategy solutions. We approach the solution of the second-stage problem by proposing a constraint-and-column generation algorithm. We show that both the constraint-generation and column-generation problems are NP-hard. Accordingly, we prescribe approximate versions of these problems that can be solved more efficiently. Our algorithm relies on solving the approximate versions until it is necessary to obtain an exact solution of the constraint-generation and column-generation problems. Then, to link the first- and second-stage problems, we model the original problem using an epigraph reformulation, which we solve using a Benders-decomposition based approach. The efficacy of our approach is demonstrated on a set of randomly generated test instances.
{{\copyright} 2022 The Authors. \textit{Networks} published by Wiley Periodicals LLC.}A finite convergence algorithm for solving linear-quadratic network games with strategic complements and bounded strategieshttps://zbmath.org/1530.911022024-04-15T15:10:58.286558Z"Passacantando, M."https://zbmath.org/authors/?q=ai:passacantando.mauro"Raciti, F."https://zbmath.org/authors/?q=ai:raciti.fabioSummary: We propose a new algorithm for solving a class of linear-quadratic network games with strategic complements and bounded strategies. The algorithm is based on the sequential solution of linear systems of equations and we prove that it finds the exact Nash equilibrium of the game after a finite number of iterations. The new algorithm is then applied to a social network model of juvenile delinquency which has been investigated recently where we also consider random perturbations of some data. Experimental results show the efficiency of the algorithm in solving large scale problems.Network games and solutions from decomposition techniqueshttps://zbmath.org/1530.911032024-04-15T15:10:58.286558Z"Sánchez-Pérez, Joss"https://zbmath.org/authors/?q=ai:sanchez-perez.joss-erickSummary: In this work we provide several decomposition techniques for the study of solutions for network games that satisfy the axioms of additivity, anonymity and homogeneity. In particular, we derive a decomposition of the vector space of network games and identify the type of problems that are relevant to the study of such solutions. We then offer several applications of this approach for solutions of network games with three and four players.Consensus through connectionshttps://zbmath.org/1530.911042024-04-15T15:10:58.286558Z"Sarkhel, Manish"https://zbmath.org/authors/?q=ai:sarkhel.manish"Gupta, Sonakshi"https://zbmath.org/authors/?q=ai:gupta.sonakshiSummary: A network formation model with linear-quadratic costs and strategic complementarities between agents highlighting group cohesion resulting from bilateral agreements is developed. Implications for stability under different network structures are discussed.Effort discrimination and curvature of contest technology in conflict networkshttps://zbmath.org/1530.911052024-04-15T15:10:58.286558Z"Sun, Xiang"https://zbmath.org/authors/?q=ai:sun.xiang"Xu, Jin"https://zbmath.org/authors/?q=ai:xu.jin|xu.jin.2"Zhou, Junjie"https://zbmath.org/authors/?q=ai:zhou.junjieSummary: In a model of interconnected conflicts on a network, we compare the equilibrium effort profiles and payoffs under two scenarios: uniform effort (UE) in which each contestant is restricted to exert the same effort across all the battles she participates, and discriminatory effort (DE) in which such a restriction is lifted. When the contest technology in each battle is of Tullock form, a surprising neutrality result holds within the class of semi-symmetric conflict network structures: both the aggregate actions and equilibrium payoffs under two regimes are the same. We also show that, in some sense, the Tullock form is necessary for such a neutrality result. Moving beyond the Tullock family, we further demonstrate how the curvature of contest technology shapes the welfare and effort effects.A cellular automaton for blocking queen gameshttps://zbmath.org/1530.911062024-04-15T15:10:58.286558Z"Cook, Matthew"https://zbmath.org/authors/?q=ai:cook.matthew"Larsson, Urban"https://zbmath.org/authors/?q=ai:larsson.urban"Neary, Turlough"https://zbmath.org/authors/?q=ai:neary.turloughSummary: We show that the winning positions of a certain type of two-player game form interesting patterns which often defy analysis, yet can be computed by a cellular automaton. The game, known as Blocking Wythoff Nim, consists of moving a queen as in chess, but always towards \((0, 0)\), and it may not be moved to any of \(k-1\) temporarily ``blocked'' positions specified on the previous turn by the other player. The game ends when a player wins by blocking all possible moves of the other player. The value of \(k\) is a parameter that defines the game, and the pattern of winning positions can be very sensitive to \(k\). As \(k\) becomes large, parts of the pattern of winning positions converge to recurring chaotic patterns that are independent of \(k\). The patterns for large \(k\) display an unprecedented amount of self-organization at many scales, and here we attempt to describe the self-organized structure that appears. This paper extends a previous study [the authors, Lect. Notes Comput. Sci. 9099, 71--84 (2015; Zbl 1432.91030)], containing further analysis and new insights into the long term behaviour and structures generated by our blocking queen cellular automaton.Combinatorial game associated to the one dimensional Schelling's model of social segregationhttps://zbmath.org/1530.911072024-04-15T15:10:58.286558Z"Goles, Eric"https://zbmath.org/authors/?q=ai:goles-chacc.eric"Gómez, Luis"https://zbmath.org/authors/?q=ai:gomez.luis-hernandez|gomez.luis-j|gomez.luis-a(no abstract)Sprague-Grundy values and complexity for LCTRhttps://zbmath.org/1530.911082024-04-15T15:10:58.286558Z"Gottlieb, Eric"https://zbmath.org/authors/?q=ai:gottlieb.eric"Krnc, Matjaž"https://zbmath.org/authors/?q=ai:krnc.matjaz"Muršič, Peter"https://zbmath.org/authors/?q=ai:mursic.peterSummary: Given an integer partition of \(n\), we consider the impartial combinatorial game LCTR in which moves consist of removing either the left column or top row of its Young diagram. We show that for both normal and misère play, the optimal strategy can consist mostly of mirroring the opponent's moves. We also establish that both LCTR and Downright are domestic as well as returnable, and on the other hand neither tame nor forced.
For both games, those structural observations allow for computing the Sprague-Grundy value any position in \(O(\log (n))\) time, assuming that the time unit allows for reading an integer, or performing a basic arithmetic operation. This improves on the previously known bound of \(O(n)\) due to \textit{J. Ilić} [``Computing Sprague-Grundy values for arbitrary partitions'', Preprint, \url{doi:10.5281/zenodo.6782383}]. We also cover some other complexity measures of both games, such as state-space complexity, and number of leaves and nodes in the corresponding game tree.Optimal schemes for combinatorial query problems with integer feedbackhttps://zbmath.org/1530.911092024-04-15T15:10:58.286558Z"Martinsson, Anders"https://zbmath.org/authors/?q=ai:martinsson.andersSummary: A \textit{query game} is a pair of a set \(Q\) of \textit{queries} and a set \(\mathcal{F}\) of functions, or \textit{codewords} \(f : Q \to \mathbb{Z} .\) We think of this as a two-player game. One player, Codemaker, picks a hidden codeword \(f \in \mathcal{F} \). The other player, Codebreaker, then tries to determine \(f\) by asking a sequence of queries \(q \in Q\), after each of which Codemaker must respond with the value \(f(q)\). The goal of Codebreaker is to uniquely determine \(f\) using as few queries as possible. Two classical examples of such games are coin-weighing with a spring scale, and Mastermind, which are of interest both as recreational games and for their connection to information theory.
In this paper, we will present a general framework for finding short solutions to query games. As applications, we give new self-contained proofs of the query complexity of variations of the coin-weighing problems, and prove new results that the deterministic query complexity of Mastermind with \(n\) positions and \(k\) colors is \(\Theta(n \log k / \log n + k)\) if only black-peg information is provided, and \(\Theta(n \log k / \log n + k / n)\) if both black- and white-peg information is provided. In the deterministic setting, these are the first up to constant factor optimal solutions to Mastermind known for any \(k \geqslant n^{1-o(1)}\).Game positions of multiple hook removing gamehttps://zbmath.org/1530.911102024-04-15T15:10:58.286558Z"Motegi, Yuki"https://zbmath.org/authors/?q=ai:motegi.yukiSummary: Multiple hook removing game (MHRG) introduced in \textit{T. Abuku} and \textit{M. Tada} [Integers 23, Paper G1, 37 p. (2023; Zbl 1514.91032)] is an impartial game played in terms of Young diagrams. In this paper, we give a characterization of the set of all game positions in MHRG. As an application, we prove that for \(t\in Z\ge 0\) and \(m,n\in N\) such that \(t\le m\le n\), and a Young diagram \(Y\) contained in the rectangular Young diagram \(Y_{t,n}\) of size \(t\times n\), \(Y\) is a game position in MHRG with \(Y_{m,n}\) the starting position if and only if \(Y\) is a game position in MHRG with \(Y_{t,n-m+t}\) the starting position, and also that the Grundy value of \(Y\) in the former MHRG is equal to that in the latter MHRG.Difference Stackelberg game theoretic model of innovations management in universitieshttps://zbmath.org/1530.911112024-04-15T15:10:58.286558Z"Kalachev, Vassily Yu."https://zbmath.org/authors/?q=ai:kalachev.vassily-yu"Ougolnitsky, Guennady A."https://zbmath.org/authors/?q=ai:ugolnitskii.gennadii-anatolevich"Usov, Anatoly B."https://zbmath.org/authors/?q=ai:usov.anatoly-bSummary: We built a two-level difference game theoretic model ``federal state universities'' in open-loop strategies. The leading player (principal) is the state or its representative bodies, the followers (agents) are competing a la Cournot universities. The agents assign their resources to the development of new online teaching courses which are considered as their innovative investments. An optimality principle from the point of view of agents is a set of Nash equilibria in their game in normal form, and from the point of view of the principal it is a solution of the direct or inverse Stackelberg game ``principal-agents''. The respective dynamic problems of conflict control are solved by means of the Pontryagin maximum principle and simulation modeling. The received results are analyzed, and the main conclusion is that two-level system of control of the innovative educational products promotion in the universities is necessary.
For the entire collection see [Zbl 1522.91009].Cost optimisation of hybrid institutional incentives for promoting cooperation in finite populationshttps://zbmath.org/1530.911122024-04-15T15:10:58.286558Z"Duong, M. H."https://zbmath.org/authors/?q=ai:duong.manh-hong"Durbac, C. M."https://zbmath.org/authors/?q=ai:durbac.c-m"Han, T. A."https://zbmath.org/authors/?q=ai:han.the-anhSummary: In this paper, we rigorously study the problem of cost optimisation of hybrid (mixed) institutional incentives, which are a plan of actions involving the use of reward and punishment by an external decision-maker, for maximising the level (or guaranteeing at least a certain level) of cooperative behaviour in a well-mixed, finite population of self-regarding individuals who interact via cooperation dilemmas (donation game or public goods game). We show that a mixed incentive scheme can offer a more cost-efficient approach for providing incentives while ensuring the same level or standard of cooperation in the long-run. We establish the asymptotic behaviour (namely neutral drift, strong selection, and infinite-population limits). We prove the existence of a phase transition, obtaining the critical threshold of the strength of selection at which the monotonicity of the cost function changes and providing an algorithm for finding the optimal value of the individual incentive cost. Our analytical results are illustrated with numerical investigations. Overall, our analysis provides novel theoretical insights into the design of cost-efficient institutional incentive mechanisms for promoting the evolution of cooperation in stochastic systems.Analysis of Boolean functions related to binary input binary output two-party nonlocal gameshttps://zbmath.org/1530.911132024-04-15T15:10:58.286558Z"Basak, Jyotirmoy"https://zbmath.org/authors/?q=ai:basak.jyotirmoy"Maitra, Subhamoy"https://zbmath.org/authors/?q=ai:maitra.subhamoy"Paul, Prabal"https://zbmath.org/authors/?q=ai:paul.prabal"Roy, Animesh"https://zbmath.org/authors/?q=ai:roy.animeshSummary: The famous CHSH game can be interpreted with Boolean functions while understanding the success probability in the classical scenario. In this paper, we have exhaustively studied all the Boolean functions on four variables to express binary input binary output two-party nonlocal games and explore their performance in both classical and quantum scenarios. Our analysis finds out some other games (other than the CHSH game) which offers a higher success probability in the quantum scenario as compared to the classical one. Naturally, our study also notes that the CHSH game (and the games corresponding to the similar partition) is the most efficient in terms of separation between quantum and classical techniques.Preventive warshttps://zbmath.org/1530.911142024-04-15T15:10:58.286558Z"Abbink, Klaus"https://zbmath.org/authors/?q=ai:abbink.klaus"Dong, Lu"https://zbmath.org/authors/?q=ai:dong.lu"Huang, Lingbo"https://zbmath.org/authors/?q=ai:huang.lingboSummary: The rise of a new power may lead the dominant power to seek a preventive war. We study this scenario in an experimental two-stage bargaining game. In each stage, the rising power makes a bargaining offer and the declining power must choose whether to accept it or fight. Between the two stages, the winning probability shifts towards the rising power. We find fewer preventive wars when the power shift is smaller and when the rising state has the commitment power. Communication and repeated interaction decrease the likelihood of preventive wars. High fighting costs almost eliminate such wars when the rising power's first-stage offer is sufficiently large.Guilt aversion in (new) games: does partners' payoff vulnerability matter?https://zbmath.org/1530.911152024-04-15T15:10:58.286558Z"Attanasi, Giuseppe"https://zbmath.org/authors/?q=ai:attanasi.giuseppe"Rimbaud, Claire"https://zbmath.org/authors/?q=ai:rimbaud.claire"Villeval, Marie Claire"https://zbmath.org/authors/?q=ai:villeval.marie-claireSummary: We investigate whether players' guilt aversion is modulated by their co-players vulnerability. In new variations of a three-player trust game, we manipulate payoff-vulnerability and endowment-vulnerability. The former (standard) vulnerability arises when a player's material payoff depends on another player's action. The latter arises when a player's initial endowment is entrusted to another player. Treatments vary whether trustees can condition their decision on the belief of a co-player who is payoff-vulnerable and/or endowment-vulnerable, or not vulnerable at all, and the decision rights of the vulnerable player. We find that trustees' guilt aversion is insensitive to both the dimension of the co-player's vulnerability and the decision rights of the co-player. Guilt is activated even absent the vulnerability of their co-players. Rather, players' guilt is triggered by the willingness to respond to their co-player's beliefs on their strategy.Predictably competitive? What faces can tell us about competitive behaviorhttps://zbmath.org/1530.911162024-04-15T15:10:58.286558Z"Balafoutas, Loukas"https://zbmath.org/authors/?q=ai:balafoutas.loukas"Fornwagner, Helena"https://zbmath.org/authors/?q=ai:fornwagner.helena"Grosskopf, Brit"https://zbmath.org/authors/?q=ai:grosskopf.britSummary: Competition for limited resources is ubiquitous in social and economic life and has sparked a large body of research on the determinants of competitive behavior. While we know a lot about the role of contextual factors and personality traits, the potential link between competitive behavior and physical appearance remains unexplored. In this study we test whether objective facial characteristics and subjective attractiveness ratings are related to the competitive behavior in the form of opting for a tournament payment scheme in a real-effort task. We find no association for any of the examined characteristics. Nevertheless, we show that individuals are significantly better than chance at predicting the competitiveness of experimental participants, just by looking at their headshots. These findings advance our understanding of the role of observable physical characteristics as telltale signs of behavior.Communication with partially verifiable information: an experimenthttps://zbmath.org/1530.911172024-04-15T15:10:58.286558Z"Burdea, Valeria"https://zbmath.org/authors/?q=ai:burdea.valeria"Montero, Maria"https://zbmath.org/authors/?q=ai:montero.maria"Sefton, Martin"https://zbmath.org/authors/?q=ai:sefton.martinSummary: We use laboratory experiments to study communication games with partially verifiable information. In these games, based on [\textit{J. Glazer} and \textit{A. Rubinstein}, Econometrica 72, No. 6, 1715--1736 (2004; Zbl 1141.91338); ``A study in the pragmatics of persuasion: a game theoretical approach'', Theor. Econ. 1, No. 4, 395--410 (2006)], an informed sender sends a two-dimensional message to a receiver, but only one dimension of the message can be verified. We investigate the effect of evidence and verification control using three treatments: one where messages are unverifiable, one where the receiver chooses which dimension to verify and one where the sender has this verification control. First, we find that evidence helps the receiver. Second, despite significant differences in behavior across the two verification treatments, receivers' payoffs do not differ significantly across these treatments, suggesting they are not hurt by delegating verification control. We also show that a theoretically optimal receiver commitment strategy identified by Glazer and Rubinstein [loc. cit.] is close to being an optimal response to senders' observed behavior in both treatments.Commitment requests do not affect truth-telling in laboratory and online experimentshttps://zbmath.org/1530.911182024-04-15T15:10:58.286558Z"Cagala, Tobias"https://zbmath.org/authors/?q=ai:cagala.tobias"Glogowsky, Ulrich"https://zbmath.org/authors/?q=ai:glogowsky.ulrich"Rincke, Johannes"https://zbmath.org/authors/?q=ai:rincke.johannes"Schudy, Simeon"https://zbmath.org/authors/?q=ai:schudy.simeonSummary: Using a standard cheating game, we investigate whether the request to sign a no-cheating declaration affects truth-telling. Our design varies the content of a no-cheating declaration (reference to ethical behavior vs. reference to possible sanctions) and the type of experiment (online vs. offline). Irrespective of the declaration's content, commitment requests do not affect truth-telling, neither in the laboratory nor online. The inefficacy of commitment requests appears robust across different samples and does not depend on psychological measures of reactance.Contests with entry fees: theory and evidencehttps://zbmath.org/1530.911192024-04-15T15:10:58.286558Z"Duffy, John"https://zbmath.org/authors/?q=ai:duffy.john"Matros, Alexander"https://zbmath.org/authors/?q=ai:matros.alexander"Valencia, Zehra"https://zbmath.org/authors/?q=ai:valencia.zehraSummary: We provide some theory and experimental evidence on contests with entry fees. In our setup, players must simultaneously decide whether or not to pay a fee to enter a contest and the amount they wish to bid should they choose to enter the contest. In a general \(n\)-bidder game, we show that the addition of contest entry fees increases the contest designer's expected revenue and that there is a unique revenue maximizing entry fee. In an experimental test of this theory we vary both the entry fee and the number of bidders. We find over-bidding for all entry fees and bidder group sizes, \(n\). We also find under-participation in the contest for low entry fees and over-participation for higher entry fees. In the case of 3 bidders, the revenue maximizing entry fee for the contest designer is found to be significantly greater than the theoretically optimal entry fee. We offer some possible explanations for these departures from theoretical predictions.Asymmetric volunteer's dilemma game: theory and experimenthttps://zbmath.org/1530.911202024-04-15T15:10:58.286558Z"Kawagoe, Toshiji"https://zbmath.org/authors/?q=ai:kawagoe.toshiji"Takizawa, Hirokazu"https://zbmath.org/authors/?q=ai:takizawa.hirokazu"Yamamori, Tetsuo"https://zbmath.org/authors/?q=ai:yamamori.tetsuoSummary: This study explores asymmetric volunteer dilemma games in which players incur different costs for volunteering. \textit{A. Diekmann} [Int. J. Game Theory 22, No. 1, 75--85 (1993; Zbl 0775.90303)] conjectures that a player with less cost is more likely to contribute at the equilibrium if it is risk dominant. We have re-examined this hypothesis theoretically and experimentally and found that even when focusing on risk-dominant equilibria, the explanatory power of the theory is not universal. An econometric comparison among several behavioral models including regret aversion shows that quantal response equilibrium best explains the data.The infinitely repeated volunteer's dilemma: an experimental studyhttps://zbmath.org/1530.911212024-04-15T15:10:58.286558Z"Kloosterman, Andrew"https://zbmath.org/authors/?q=ai:kloosterman.andrew"Mago, Shakun"https://zbmath.org/authors/?q=ai:mago.shakunSummary: We examine how repeated interaction can facilitate coordinated turn-taking in a two-player infinitely repeated volunteer's dilemma. We conjecture that repetition creates an environment for players to coordinate on the Pareto efficient, but asymmetric pure strategy Nash equilibria of the stage game by taking turns volunteering. We consider three cost treatments: both players have the same cost; one player has a higher cost and this cost assignment is constant; one player has a higher cost and this cost assignment is random. We find that turn-taking is the dominant play when costs are symmetric. When costs are asymmetric, the low-cost player is more likely to volunteer. However, contrary to predictions, asymmetric randomly allocated costs do not perfectly coordinate turn-taking. When costs are asymmetric and constant over time, behavior is markedly heterogeneous.Dynamic structure in a four-strategy game: theory and experimenthttps://zbmath.org/1530.911222024-04-15T15:10:58.286558Z"Zhijian, Wang"https://zbmath.org/authors/?q=ai:zhijian.wang"Zhou, Shujie"https://zbmath.org/authors/?q=ai:zhou.shujie"Qinmei, Yao"https://zbmath.org/authors/?q=ai:qinmei.yao"Yijia, Wang"https://zbmath.org/authors/?q=ai:yijia.wang"Gang, Pan"https://zbmath.org/authors/?q=ai:gang.panSummary: Game dynamics theory, as any field of science, the consistency between theory and experiment is essential. In the past 10 years, important progress has been made in the merging of the theory and experiment in this field, in which dynamics cycle is the presentation. However, the achievement failed to eliminate the constraints of the Euclidean two-dimensional cycle. This paper uses a classic four-strategy game to study the dynamic structure (non-Euclidean superplane cycle). The consistency is in significant between the three ways: (1) analytical results from evolutionary dynamics equations, (2) agent-based simulation results from learning models and (3) laboratory results from human subjects game experiments. The consistency suggests that, the game dynamic structure could be quantitatively predictable, observable, and controllable in general.
For the entire collection see [Zbl 1522.91009].Computing a mechanism for a Bayesian and partially observable Markov approachhttps://zbmath.org/1530.911252024-04-15T15:10:58.286558Z"Clempner, Julio B."https://zbmath.org/authors/?q=ai:clempner.julio-b"Poznyak, Alexander S."https://zbmath.org/authors/?q=ai:poznyak.alexander-sSummary: The design of incentive-compatible mechanisms for a certain class of finite Bayesian partially observable Markov games is proposed using a dynamic framework. We set forth a formal method that maintains the incomplete knowledge of both the Bayesian model and the Markov system's states. We suggest a methodology that uses Tikhonov's regularization technique to compute a Bayesian Nash equilibrium and the accompanying game mechanism. Our framework centers on a penalty function approach, which guarantees strong convexity of the regularized reward function and the existence of a singular solution involving equality and inequality constraints in the game. We demonstrate that the approach leads to a resolution with the smallest weighted norm. The resulting individually rational and ex post periodic incentive compatible system satisfies this requirement. We arrive at the analytical equations needed to compute the game's mechanism and equilibrium. Finally, using a supply chain network for a profit maximization problem, we demonstrate the viability of the proposed mechanism design.Signaling, screening, and core stabilityhttps://zbmath.org/1530.911272024-04-15T15:10:58.286558Z"Kamishiro, Yusuke"https://zbmath.org/authors/?q=ai:kamishiro.yusuke"Vohra, Rajiv"https://zbmath.org/authors/?q=ai:vohra.rajiv"Serrano, Roberto"https://zbmath.org/authors/?q=ai:serrano.robertoSummary: This paper provides a noncooperative approach to core stability in an economy with incomplete information. We study the perfect Bayesian equilibria of an extensive form mechanism that extends the one used by \textit{R. Serrano} and \textit{R. Vohra} [Soc. Choice Welfare 14, No. 4, 513--525 (1997; Zbl 0888.90030)] to implement the core of a complete-information economy. This leads to a version of the core that we refer to as the \textit{sequential core}, which allows for information to be transmitted among the agents during the process of coalition formation. Such information flows include proposals that can be viewed as signaling devices and/or screening contracts. Equilibrium refinements are then used to provide justifications for the coarse core and the fine core. As a robustness check, we show that the sequential core corresponds to stationary PBE outcomes of an infinite horizon bargaining game.Behavioral strong implementationhttps://zbmath.org/1530.911392024-04-15T15:10:58.286558Z"Hayashi, T."https://zbmath.org/authors/?q=ai:hayashi.takashi"Jain, R."https://zbmath.org/authors/?q=ai:jain.ritesh"Korpela, V."https://zbmath.org/authors/?q=ai:korpela.ville"Lombardi, M."https://zbmath.org/authors/?q=ai:lombardi.micheleSummary: Choice behavior is rational if it is based on the maximization of some context-independent preference relation. This study re-examines the questions of implementation theory in a setting where players' choice behavior need not be rational and coalition formation must be taken into account. Our model implies that with non-rational players, the formation of groups greatly affects the design exercise. As a by-product, we also propose a notion of behavioral efficiency and we compare it with existing notions.An adaptive optimization consensus mechanism for group decision making using the Shapley allocation schemehttps://zbmath.org/1530.911452024-04-15T15:10:58.286558Z"Meng, Fanyong"https://zbmath.org/authors/?q=ai:meng.fanyong"Zhao, Dengyu"https://zbmath.org/authors/?q=ai:zhao.dengyu"Tan, Chunqiao"https://zbmath.org/authors/?q=ai:tan.chunqiaoSummary: Adaptive consensus mechanism adopts differentiating consensus improvement strategies according to different consensus levels, which is reasonable and efficient for reaching consensus in group decision making. However, previous adaptive consensus methods adopt the feedback iteration mechanism, which has drawbacks such as time-consuming, over-consensus adjustment, and failure of consensus-reaching. Therefore, this paper studies the adaptive consensus mechanism by optimization models to avoid the above issues of the feedback iteration mechanism. In our approach, corresponding optimization models are constructed to identify non-consensus judgments, non-consensus alternatives, and non-consensus decision makers, respectively. Meanwhile, the related total minimum consensus adjustments are ascertained. Since the uniqueness of the consensus adjustment scheme cannot be ensured according to the built models, we regard it as a cost allocation problem in cooperative games, and define three types of consensus adjustment cooperative games. After that, the Shapley function, a well-known single payoff index, is adopted to allocate total consensus adjustments in different cases. Additionally, we employ the optimization model to determine the modified values of non-consensus judgments by minimizing the number of adjustment judgments. Finally, numerical study and comparison are made.Location games with referenceshttps://zbmath.org/1530.911602024-04-15T15:10:58.286558Z"Fournier, Gaëtan"https://zbmath.org/authors/?q=ai:fournier.gaetan"Francou, Amaury"https://zbmath.org/authors/?q=ai:francou.amaurySummary: We study a class of location games where players want to attract as many resources as possible and pay a cost when deviating from an exogenous reference location. This class of games includes political competitions between policy-interested parties and firms' costly horizontal differentiation. We find that the introduction of reference locations simplifies the set of pure-strategy equilibrium to a unique candidate which has a strong property: at most four players, the two most-left and two most-right, deviate from their reference locations. We provide necessary and sufficient conditions for the candidate to be an equilibrium. We illustrate our results in particular cases including the duopoly competition where we moderate the principle of minimal differentiation.Voting with interdependent values: the Condorcet winnerhttps://zbmath.org/1530.911612024-04-15T15:10:58.286558Z"Gershkov, Alex"https://zbmath.org/authors/?q=ai:gershkov.alex"Kleiner, Andreas"https://zbmath.org/authors/?q=ai:kleiner.andreas"Moldovanu, Benny"https://zbmath.org/authors/?q=ai:moldovanu.benny"Shi, Xianwen"https://zbmath.org/authors/?q=ai:shi.xianwenSummary: We generalize the standard, private values voting model with single-peaked preferences and incomplete information by introducing interdependent preferences. Our main results show how standard mechanisms that are outcome-equivalent and implement the Condorcet winner under complete information or under private values yield starkly different outcomes if values are interdependent. We also propose a new notion of Condorcet winner under incomplete information and interdependent preferences, and discuss its implementation. The new phenomena in this paper arise because different voting rules (including dynamic ones) induce different processes of information aggregation and learning.Abstention and informedness in nonpartisan electionshttps://zbmath.org/1530.911652024-04-15T15:10:58.286558Z"Meyer, Jacob"https://zbmath.org/authors/?q=ai:meyer.jacob-m"Rentschler, Lucas"https://zbmath.org/authors/?q=ai:rentschler.lucasSummary: We develop and experimentally test a model of voter information acquisition in nonpartisan elections, both with and without abstention. We theoretically demonstrate that allowing for abstention can increase information acquisition, provided the cost of information is not too low. Our experimental data find that voters are less responsive than predicted to increases in the cost of information. As a result, the cost required to yield higher levels of informedness when abstention is allowed is higher than predicted. Our data are well explained by agent quantal response equilibrium, which accounts for the fact that uninformed voters are often observed to vote, even when it is not rational to do so.Social capital and the status externalityhttps://zbmath.org/1530.911782024-04-15T15:10:58.286558Z"Itaya, Jun-ichi"https://zbmath.org/authors/?q=ai:itaya.jun-ichi"Tsoukis, Christopher"https://zbmath.org/authors/?q=ai:tsoukis.christopherSummary: This paper investigates how the presence of social capital affects the externality arising from status-seeking preference as a parable for inefficient antagonistic behavior. It is assumed that the stock of social capital accumulates through the strategic interaction among a finite number of rational, infinitely-lived individuals. Using a differential game, we show that there are two types of Markov perfect equilibrium strategy, of which one leads a society to zero social capital, while the other leads to the satiation level of social capital. When there is an unstable interior steady state, there is a threshold: with any initial stock of social capital above (below) that, society is able to build social capital (get stuck in a poverty trap of null social capital). In the latter case, the intervention of governments is called upon, because social welfare in the poverty trap is less than that in the social capital-rich society.
{{\copyright} 2020 IAET}Real-time monitoring in a public-goods gamehttps://zbmath.org/1530.911902024-04-15T15:10:58.286558Z"He, Simin"https://zbmath.org/authors/?q=ai:he.simin"Zhu, Xun"https://zbmath.org/authors/?q=ai:zhu.xunSummary: We investigate a novel continuous-time mechanism in a public-goods game. In this game, a clock ensures that the contributions regularly increase within a fixed period for each player. The players can choose when to stop their contributions from increasing while others observe their actions in real time. We demonstrate, theoretically and experimentally, that such a mechanism effectively improves contributions. Three critical factors could cause improvement: announcements, incremental commitments, and the clock. We further decompose these factors and find that while announcements alone are ineffective, introducing incremental commitments and the clock can significantly improve contributions.Disclosure of quality preference-revealing information in a supply chain with competitive productshttps://zbmath.org/1530.912032024-04-15T15:10:58.286558Z"Sun, Fei"https://zbmath.org/authors/?q=ai:sun.fei|sun.fei.1"Yang, Hui"https://zbmath.org/authors/?q=ai:yang.hui.2|yang.hui.4"Chen, Jing"https://zbmath.org/authors/?q=ai:chen.jing.4|chen.jing.12|chen.jing.2|chen.jing|chen.jing.7|chen.jing.5|chen.jing.3"Wang, Fa"https://zbmath.org/authors/?q=ai:wang.faSummary: We examine price setting and the decision to disclose quality preference-revealing information in a supply chain with two competing manufacturers supplying two quality-differentiated products to a common retailer. Consumers have complete knowledge of product quality but are uncertain about how the quality will match their own preferences. We study who should provide preference-revealing information to help consumers understand their own quality preferences, and how such information disclosure affects horizontal and vertical competitions in the supply chain. We show that the manufacturer with a higher unit quality production cost has a higher incentive to provide such information, and we show how each supply chain member sets its information policy. The role of information releaser will switch from an upstream member (a manufacturer) to the downstream member (the retailer) as the market information level (the consumer's degree of informativeness before disclosure) increases. Information disclosure softens both horizontal and vertical competitions in the supply chain. We extend our model to examine the case in which the two manufacturers make simultaneous decisions, and the case when a supply chain member incurs a cost for implementing information disclosure.The optimal product pricing and carbon emissions reduction profit allocation of CET-covered enterprises in the cooperative supply chainhttps://zbmath.org/1530.912062024-04-15T15:10:58.286558Z"Zhang, Yue-Jun"https://zbmath.org/authors/?q=ai:zhang.yue-jun"Sun, Ya-Fang"https://zbmath.org/authors/?q=ai:sun.ya-fang"Huo, Bao-Feng"https://zbmath.org/authors/?q=ai:huo.bao-fengSummary: The carbon quota allocation rules of China's pilot carbon emissions trading (CET) regions are various, which mainly include benchmarking, historical carbon intensity reduction and auctioning. When the allocation rules change, it is unresolved how to achieve the optimal product prices and effectively allocate the carbon emissions reduction profits of CET-covered enterprises in the cooperative supply chain. Thus, this paper uses the Stackelberg game, Nash equilibrium and the Shapley value based on cost modification to investigate these issues. The results indicate that: (1) The increasing carbon prices can always improve the retail prices only under the auctioning rule. Meanwhile, the growing low-carbon awareness of consumer cannot be always conducive to improving the wholesale and retail prices, and the similar product prices of non-CET-covered enterprises have greater impact on the wholesale prices than that on the retail prices. (2) Only under the free carbon quota allocation rules, can the optimal wholesale and retail prices under the Stackelberg game be always higher than those under the Nash equilibrium. Meanwhile, the auctioning rule can better reduce carbon emissions than the free allocation rules. (3) Improving carbon emissions reduction contribution and emission reduction costs can be conducive to increasing the carbon emission reduction profits of the supplier and retailer, while the impact of carbon emission reduction contribution on improving the carbon emission reduction profits is not always greater than that of the carbon emission reduction costs.Optimal disclosure in all-pay auctions with interdependent valuationshttps://zbmath.org/1530.912132024-04-15T15:10:58.286558Z"Chen, Bo"https://zbmath.org/authors/?q=ai:chen.bo.11|chen.bo.4|chen.bo.3|chen.bo.6|chen.bo.2|chen.bo"Chen, Bo"https://zbmath.org/authors/?q=ai:chen.bo.2|chen.bo.6|chen.bo|chen.bo.4|chen.bo.3|chen.bo.11Summary: We study all-pay auctions with one-sided private information and interdependent valuations. To sharpen the competition and maximize revenue, the auction organizer can design an information disclosure policy through Bayesian persuasion about the bidder with private information. We characterize optimal disclosure and find that optimal disclosure exhibits \textit{almost} full disclosure, where the uninformed bidder can always narrow the informed bidder's private information down to at most two types. We also illustrate our characterization in a simple binary-type setting and investigate issues such as comparative statics, welfare, and efficiency.The equilibrium of the bargaining game and core convergence theorem on an exchange economy with limited tradershttps://zbmath.org/1530.912142024-04-15T15:10:58.286558Z"Chen, Jianguo"https://zbmath.org/authors/?q=ai:chen.jianguoSummary: \textit{G. Debreu} and \textit{H. Scarf} [Int. Econ. Rev. 4, 235--246 (1963; Zbl 0122.37702)], \textit{W. Hildenbrand} [Core and equilibria of a large economy. Princeton Studies in Mathematical Economics. 5. Princeton, N.J.: Princeton University Press. (1974; Zbl 0351.90012)], \textit{R. J. Aumann} [Econometrica 32, 39--50 (1964; Zbl 0137.39003)]), \textit{H. Dierker} [J. Math. Econ. 2, 155--169 (1975; Zbl 0321.90011)], \textit{T. F. Bewley} [Econometrica 41, 425--454 (1973; Zbl 0271.90007)], and others have shown that the core of an exchange economy with infinitely many or finitely many traders converges. However, an exchange economy does not always consist of infinitely many or finitely many traders. This note provides proof of the core convergence theorem on an exchange economy with limited traders by a bargaining game methodology. The main contribution of this note is to innovate the equilibrium solution to the bargaining game in the exchange economy. In this note, the concept of common payoff is introduced; in the bargaining game of a coalition on its common payoff, all coalition members will get the same distribution, thus the distribution scheme of the cooperation surplus of the exchange economy is determined.
This note shows that the bargaining game among the traders on the distribution of the cooperation surplus will make the pure exchange economy with limited traders converge to the Walrasian equilibrium, all the allocations other than the Walrasian equilibrium will be eliminated from the core of this economy.
{{\copyright} 2022 The Authors. \textit{Bulletin of Economic Research} published by Trustees of the Bulletin of Economic Research and John Wiley \& Sons Ltd.}Efficient liability in expert marketshttps://zbmath.org/1530.912152024-04-15T15:10:58.286558Z"Chen, Yongmin"https://zbmath.org/authors/?q=ai:chen.yongmin"Li, Jianpei"https://zbmath.org/authors/?q=ai:li.jianpei"Zhang, Jin"https://zbmath.org/authors/?q=ai:zhang.jin.8Summary: When providing professional services, an expert may misbehave by either prescribing ``wrong'' treatment for consumer's problem or failing to exert proper effort to diagnose it. We show that under a range of liabilities the expert will recommend the appropriate treatment based on his private information if markups for alternative treatments are close enough; however, a well-designed liability rule is essential for also motivating efficient diagnosis effort. We further demonstrate that unfettered price competition between experts may undermine the efficient role of liability, whereas either a minimum-price constraint or an obligation-to-serve requirement can restore it.
{{\copyright} (2022) by the Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.}Network externalities, dominant value margins, and equilibrium uniquenesshttps://zbmath.org/1530.912162024-04-15T15:10:58.286558Z"Choi, Jay Pil"https://zbmath.org/authors/?q=ai:choi.jay-pil"Stefanadis, Christodoulos"https://zbmath.org/authors/?q=ai:stefanadis.christodoulosSummary: We examine tippy network markets that accommodate price discrimination. The analysis shows that when a mild equilibrium refinement, the monotonicity criterion, is adopted, network competition may have a unique subgame-perfect equilibrium regarding the winner's identity; the prevailing brand may be fully determined by its product features. We bring out the concept of the dominant value margin, which is a metric of the effectiveness of divide-and-conquer strategies. The supplier with the larger dominant value margin may always sell to all customers in equilibrium. Such a market outcome is not necessarily socially efficient.
{{\copyright} (2022) by the Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.}Spying and imperfect commitment in first-price auctions: a case of tacit collusionhttps://zbmath.org/1530.912192024-04-15T15:10:58.286558Z"Fan, Cuihong"https://zbmath.org/authors/?q=ai:fan.cuihong"Jun, Byoung Heon"https://zbmath.org/authors/?q=ai:jun.byoung-heon"Wolfstetter, Elmar G."https://zbmath.org/authors/?q=ai:wolfstetter.elmar-gIn this article, the authors examine the impact of spying in a first-price auction, assuming the spied-at bidder may secretly revise his bid with some known probability. The collusive impact suggests that once a bidder has procured the service of a spy, the spied-at bidder passively tolerates being spied-at by not taking measures to neutralize the spy and by not firing the spy if his identity has become known. It is shown that this collusive impact shows up in all equilibria and is strongest in the unique pooling equilibrium which is also payoff dominant. Section 2 presents the binary base model. Section 3 summarizes two benchmark games: the game with perfectly informative and with uninformative signals. In Section 4, the authors solve the game with imperfect commitment that yields imperfectly informative signals and fully characterize the unique pooling equilibrium and the family of partially separating equilibria. Section 5 summarizes the collusive impact of spying under imperfect commitment on players' payoffs and offers an intuitive interpretation.
Reviewer: Nikolay Kyurkchiev (Plovdiv)Bargaining power in crisis bargaininghttps://zbmath.org/1530.912242024-04-15T15:10:58.286558Z"Leventoğlu, Bahar"https://zbmath.org/authors/?q=ai:leventoglu.baharSummary: A large body of game-theoretic work examines the process by which uncertainty can lead to inefficient war. In a typical crisis bargaining model, players negotiate according to a pre-specified game form and no player has the ability to change the rules of the game. However, when one of the parties has full bargaining power and is able to set the rules of the game on her own, the game itself becomes an endogenous decision variable. I formulate this problem in a principal-agent framework. I show that both the likelihood of costly war and the exact mechanism that yields it depend on the nature of the informational problem and the identity of the informed player.Does risk aversion explain behavior in a lemon market?https://zbmath.org/1530.912252024-04-15T15:10:58.286558Z"Lin, Lihui"https://zbmath.org/authors/?q=ai:lin.lihuiSummary: \textit{S. Siegenthaler} [Games Econ. Behav. 102, 147--161 (2017; Zbl 1409.91078)] proposes an ingenious solution to the lemon market adverse selection problem. He incorporates ``cheap talk'' in which sellers send out costless and nonbinding messages informing potential buyers of the quality of their goods; these messages could be true or false. This segments the market into several submarkets. Potential buyers need to decide which submarket to enter and what price to bid for the goods. Sellers then decide whether to accept the bid or not. He experimentally tests his model and finds that the comparative static results align with his theory, although the data do not exactly fit the model. Indeed, he does not fit the model to the data. His theory assumes risk-neutral decision-makers (DMs). Two reasons why the fit is not perfect may be that the DMs are not risk neutral and not perfectly rational. In this note, we report the results of fitting an asymmetric risk averse quantal response equilibrium (QRE) extension of his model to his data, and we find that the extension fits well. We show that the results are consistent with the market evidence and shed light on future research on lemon markets.
{{\copyright} 2022 The Authors. \textit{Bulletin of Economic Research} published by Trustees of the Bulletin of Economic Research and John Wiley \& Sons Ltd.}The bargaining set and coalition formationhttps://zbmath.org/1530.912292024-04-15T15:10:58.286558Z"Shimomura, Ken-Ichi"https://zbmath.org/authors/?q=ai:shimomura.ken-ichiSummary: We study solution concepts for nontransferable utility games according to which the coalition structure and the payoff allocations are simultaneously determined. The \textit{steady bargaining set} is a refinement of the Zhou bargaining set, which is included in the Mas-Colell bargaining set. We prove the nonemptiness and partial efficiency of the steady bargaining set for at least one coalition structure under the \textit{restrictive non-crossing condition}. Without this condition, the Zhou bargaining set may be empty and the Mas-Colell bargaining set is nonempty but may not be efficient.
{{\copyright} 2021 International Association for Economic Theory}Losing money to make money: the benefits of redistribution in collective bargaining in sportshttps://zbmath.org/1530.912312024-04-15T15:10:58.286558Z"Vohra, Akhil"https://zbmath.org/authors/?q=ai:vohra.akhilSummary: I develop a model of majority-rule collective bargaining between a sports league and its players when delay costs incurred by players are wealth-dependent. I propose a refinement of subgame perfect equilibrium that requires equilibrium strategies to be immune to deviations by any majority subgroup. I show this is equivalent to giving the player with median bargaining power the unilateral ability to negotiate with the league. Using this model, I demonstrate that policies reallocating surplus from high-talent to moderate-talent players, such as maximum contracts in professional sports, can improve the welfare of \textit{all} players. Redistribution of surplus harmonizes players' interests, giving a majority of them a greater stake in the bargaining outcome. The model highlights the gains to be had if a heterogeneous group agrees to concessions that increase the alignment of their individual interests.Solution of the meeting time choice problem for \(n\) personshttps://zbmath.org/1530.912352024-04-15T15:10:58.286558Z"Yashin, Vladimir V."https://zbmath.org/authors/?q=ai:yashin.vladimir-vSummary: We consider a game-theoretic model of negotiations of \(n\) persons about a meeting time. The problem is to determine the time of the meeting, with the consensus of all players required to make a final decision. The solution is found by backward induction in the class of stationary strategies. Players' wins are represented by piecewise linear functions having one peak. An subgame perfect equilibrium for the problem in the case of \(\delta\leqslant\frac 12\) is found in analytical form.
For the entire collection see [Zbl 1522.91009].Competitor referral by platformshttps://zbmath.org/1530.912372024-04-15T15:10:58.286558Z"Zhang, Jianqiang"https://zbmath.org/authors/?q=ai:zhang.jianqiang"Cao, Qingning"https://zbmath.org/authors/?q=ai:cao.qingning"He, Xiuli"https://zbmath.org/authors/?q=ai:he.xiuliSummary: Online platforms provide sellers' products on their websites and earn a commission fee for each unit sold. Recently, many platforms have tried to refer customers to their direct competitors. In this paper, we explain this counter-intuitive practice by developing a game-theoretic model where two competing platforms contracting with one common seller or two competing sellers. We first analyze a benchmark case where platforms and sellers are integrated, finding that competitor referral will aggregate competition and thus neither platform is willing to refer its competitor voluntarily. However, when each platform serves as a marketplace for an independent seller, it is possible that a platform voluntarily refers its competitor. The rationale is that there exists a double marginalization problem when platforms set commission fees and sellers set prices, resulting in low efficiency of product selling. By referring visitors to their competitors, platforms can introduce cannibalization to cope with the double marginalization problem. We also investigate the case when the two platforms serve one common seller, finding that as long as the seller does not charge discriminated prices for the same product, the platforms may also apply referral. This is because the benefits of the two platforms are more aligned when the common seller sets a common price. Thus, online referral which helps the competitor may also help the referring platform itself. This paper also makes sereval extensions to check the robustness of the model.Preference revelation games and strict cores of multiple-type housing market problemshttps://zbmath.org/1530.912442024-04-15T15:10:58.286558Z"Feng, Di"https://zbmath.org/authors/?q=ai:feng.di"Klaus, Bettina"https://zbmath.org/authors/?q=ai:klaus.bettinaSummary: We consider multiple-type housing market problems as introduced by \textit{H. Moulin} [Cooperative microeconomics: a game-theoretic introduction. Princeton, NJ: Princeton University Press (1995; \url{https://press.princeton.edu/books/hardcover/9780691636573/cooperative-microeconomics})] and study the relationship between strict strong Nash equilibria and the strict core (two solution concepts that are defined in terms of the absence of weak blocking coalitions). We prove that for lexicographically separable preferences, the set of all strict strong Nash equilibrium outcomes of each preference revelation game that is induced by a strictly core stable mechanism is a subset of the strict core, but not vice versa, that is, there are strict core allocations that cannot be implemented in strict strong Nash equilibrium. This result is extended to a more general set of preference domains that satisfy strict core non-emptiness and a minimal preference domain richness assumption.
{{\copyright} 2021 The Authors. \textit{International Journal of Economic Theory} published by John Wiley \& Sons Australia, Ltd on behalf of International Association for Economic Theory.}Sharing cost of network among users with differentiated willingness to payhttps://zbmath.org/1530.912512024-04-15T15:10:58.286558Z"Panova, Elena"https://zbmath.org/authors/?q=ai:panova.elena-yuSummary: We consider the problem of sharing the cost of a fixed tree-network among users with differentiated willingness to pay for the good supplied through the network. We find that the associated value-sharing problem is convex, hence, the core is large and we axiomatize a new, computationally simple core selection based on the idea of proportionality.Export versus FDI: learning through propinquityhttps://zbmath.org/1530.912582024-04-15T15:10:58.286558Z"Creane, Anthony"https://zbmath.org/authors/?q=ai:creane.anthony"Miyagiwa, Kaz"https://zbmath.org/authors/?q=ai:miyagiwa.kazSummary: This paper considers the strategic role learning plays on the choice between FDI and export under demand and cost uncertainty. FDI allows a foreign firm to learn local demand, which is beneficial. However, as it buys inputs from the same local input markets as the rival home firm, two firms' costs become perfectly correlated, which we prove harmful to the foreign firm. Thus, the interplay of the demand acquisition and the cost correlation effect affects FDI decisions. We show that FDI is more likely to occur when firms produce more differentiated goods and that FDI almost always reduces host country welfare.
{{\copyright} IAET}Equilibrium effort in games with homogeneous production functions and homogeneous valuationhttps://zbmath.org/1530.912622024-04-15T15:10:58.286558Z"Ferrarese, Walter"https://zbmath.org/authors/?q=ai:ferrarese.walterSummary: In this study, I analyze games in which the functions mapping a vector of efforts into each player's share of the prize and its value exhibit an arbitrary degree of homogeneity. I present a simple way to compute the equilibrium strategy and sufficient conditions for a unique interior symmetric pure-strategy Nash equilibrium. The setup nests \textit{D. A. Malueg} and \textit{A. J. Yates} [Economic Theory volume 27, No. 3, 719--727 (2006; \url{doi:10.1007/s00199-004-0554-9})], who exploit homogeneity for rent-seeking contests with exogenous prize valuation, and shows that homogeneity can be used to solve (i) a wider range of rent-seeking contests and (ii) other classes of games, like Cournot games with nonlinear inverse demand and possibly non homogeneous goods.
{{\copyright} 2021 The Authors. \textit{International Journal of Economic Theory} published by John Wiley \& Sons Australia, Ltd on behalf of International Association for Economic Theory.}License and entry strategies for an outside innovator in Stackelberg duopoly with royalty and fixed fee under vertical differentiationhttps://zbmath.org/1530.912662024-04-15T15:10:58.286558Z"Hattori, Masahiko"https://zbmath.org/authors/?q=ai:hattori.masahiko"Tanaka, Yasuhito"https://zbmath.org/authors/?q=ai:tanaka.yasuhitoSummary: We examine a choice of options for an outside innovating firm in Stackelberg duopoly under vertical differentiation. The options for an innovating firm are to enter the market with or without licensing its technology for producing a higher-quality good by a combination of royalty and fixed license fee, and to license its technology without entry. When the innovating firm licenses its technology to the incumbent firm without entry, its optimal royalty rate is zero. When the innovating firm enters the market with a license to the incumbent firm, and the cost function is strictly concave, its optimal royalty rate is one such that the incumbent firm drops out of the market with a negative fixed license fee. If the cost function is strictly convex, there is an internal solution of the positive optimal royalty rate with positive or negative fixed license fee. Without entry cost, if the cost function is strictly concave, the entry without license and entry with license strategies are optimal, and if it is strictly convex, the entry with license strategy is optimal.
{{\copyright} 2019 IAET}Licensing cost-reducing innovations under supply function competitionhttps://zbmath.org/1530.912712024-04-15T15:10:58.286558Z"Saglam, Ismail"https://zbmath.org/authors/?q=ai:saglam.ismailSummary: In this paper, we study the licensing of cost-reducing innovations in a duopoly under supply function competition. We show that the innovator prefers fixed-fee licensing to no licensing if its cost advantage is not extremely large. Moreover, if its cost advantage is not extremely small, the innovator prefers fixed-fee licensing and mixed licensing to revenue-royalty licensing. This second result arises only because of our assumption that the cost functions are quadratic. We show that if the cost functions are linear and royalty payments are per unit of output, the innovator strictly prefers royalty licensing to fixed-fee licensing. We also show that in our model, consumer surplus is remarkably higher under any type of licensing than under no licensing. However, revenue-royalty licensing is slightly superior for consumers to the other two types of licensing and only so if the cost advantage of the innovator is sufficiently large.
{{\copyright} 2022 Board of Trustees of the Bulletin of Economic Research and John Wiley \& Sons Ltd.}Online-offline competition with heterogeneous consumers: an example for no existence of pure strategy Nash equilibriumhttps://zbmath.org/1530.913002024-04-15T15:10:58.286558Z"Ford, Weixing"https://zbmath.org/authors/?q=ai:ford.weixing"Han, Haipeng"https://zbmath.org/authors/?q=ai:han.haipeng"Zheng, Jie"https://zbmath.org/authors/?q=ai:zheng.jieSummary: Existing literature on competition between online and offline firms has focused on market conditions that guarantee the existence of a pure strategy Nash equilibrium. In this note, by constructing a concrete example, we provide a first attempt to show that the equilibrium existence result does not necessarily hold when consumers' preferences are heterogeneous. Specifically, we consider the competition between one online firm and several offline firms in a market organized as a salop model, where consumers' preferences have a binary distribution. We identify a boundary scenario where the type distribution is binary with one type of consumer loyal to online shopping and the other type loyal to offline shopping. We show that there is no pure strategy Nash equilibrium for this boundary scenario, which indicates that the market may not be stable under such conditions. Our study contributes to a better understanding of the equilibrium existence conditions for the online versus offline retail competition.
For the entire collection see [Zbl 1522.91009].Bad reputation with simple rating systemshttps://zbmath.org/1530.913062024-04-15T15:10:58.286558Z"Lorecchio, Caio"https://zbmath.org/authors/?q=ai:lorecchio.caio"Monte, Daniel"https://zbmath.org/authors/?q=ai:monte.danielSummary: We consider information censoring through finite memory as a device against bad reputational concerns. Our class of constrained information policies resembles common practices in online reputation systems, on which customers increasingly rely whenever hiring experts. In a world of repeated interactions between a long-lived expert and short-lived customers, \textit{J. C. Ely} and \textit{J. Välimäki} [Q. J. Econ. 118, No. 3, 785--814 (2003; Zbl 1069.91014)] show that unlimited record-keeping may induce the expert to overchoose a certain action, seeking reputational gains. Consequently, welfare may reduce and markets may break down. We show that simple rating systems in such world help overcome market failures and improve upon both the full-memory and the no-memory cases.Influential news and policy-makinghttps://zbmath.org/1530.913092024-04-15T15:10:58.286558Z"Vaccari, Federico"https://zbmath.org/authors/?q=ai:vaccari.federicoSummary: This paper analyzes the implications of interventions that affect the costs of misreporting. I study a model of communication between an uninformed voter and a media outlet that knows the quality of two competing candidates. The alternatives available to the voter are endogenously championed by the two candidates. I show that higher costs may lead to more misreporting and persuasion, whereas low costs result in full revelation. The voter may be better off when less informed because of higher costs. When the media receives policy-independent gains, interventions that increase misreporting costs never directly harm the voter. However, lenient interventions that increase these costs by small amounts can be wasteful of public resources. Regulation produced by politicians leads to suboptimal interventions.Refinement of dynamic equilibrium using small random perturbationshttps://zbmath.org/1530.913152024-04-15T15:10:58.286558Z"Araujo, Aloisio"https://zbmath.org/authors/?q=ai:araujo.aloisio-p"Maldonado, Wilfredo L."https://zbmath.org/authors/?q=ai:maldonado.wilfredo-l"Pinheiro, Diogo"https://zbmath.org/authors/?q=ai:pinheiro.diogo"Pinto, Alberto A."https://zbmath.org/authors/?q=ai:pinto.alberto-adrego"Choubdar Soltanahmadi, Mohammad"https://zbmath.org/authors/?q=ai:choubdar-soltanahmadi.mohammadSummary: We propose a refinement process of dynamic equilibria based on small random perturbations (SRPs) of the backward perfect foresight (bpf) equilibrium map in a class of one-step, forward-looking dynamic models. An equilibrium is selected if its stationary measure is the limit of the stationary measures associated with the processes generated by the SRPs of the bpf maps, as the perturbation size approaches 0. We show that, for full measure sets of parameter values of a large class of one-parameter families of unimodal bpf maps, only determinate cycles or the chaotic sunspot equilibrium defined by \textit{A. P. Araujo} and \textit{W. L. Maldonado} [Econ. Theory 15, No. 1, 163--184 (2000; Zbl 1081.91561)] is selected. Two examples are provided illustrating such refinement process.
{{\copyright} 2020 International Association for Economic Theory}First mover advantage by product proliferation in multiproduct duopolyhttps://zbmath.org/1530.913182024-04-15T15:10:58.286558Z"Cheng, Yi-Ling"https://zbmath.org/authors/?q=ai:cheng.yi-ling"Tabuchi, Takatoshi"https://zbmath.org/authors/?q=ai:tabuchi.takatoshiSummary: This study aims to show that the product proliferation strategy in multi-product duopoly is first-mover advantage. We consider simultaneous and Stackelberg variety competitions. A firm producing more varieties charges a higher price, produces larger total quantities, and earns higher total revenue. When firms sequentially choose the masses of varieties and then simultaneously decide prices, the leader produces more varieties and enjoys first-mover advantage. The masses of varieties can be regarded as strategic substitutes in the same way that quantities are. Finally, the market is likely to provide too few varieties relative to the social optimum.
{{\copyright} 2019 IAET}Corruption, market quality, and entry deterrence in emerging economieshttps://zbmath.org/1530.913232024-04-15T15:10:58.286558Z"Dastidar, Krishnendu Ghosh"https://zbmath.org/authors/?q=ai:dastidar.krishnendu-ghosh"Yano, Makoto"https://zbmath.org/authors/?q=ai:yano.makotoSummary: In many emerging economies incumbent firms often use dubious means to deter entry of other firms. We analyze this scenario in a three-stage game of entry deterrence. The incumbent has incomplete information about the entrant's costs but can increase this cost by resorting to unfair means (e.g. bribing a politician who harms the entrant). We completely characterize the optimal bribe and show that this depends on the ``fairness index'' and the ``differentiation'' parameter. We also show that zero bribes need not maximize welfare and market quality. Our results seem to be compatible with anecdotal evidence from emerging economies such as India.
{{\copyright} 2020 IAET}Joint market dominance through exclusionary compatibilityhttps://zbmath.org/1530.913252024-04-15T15:10:58.286558Z"Do, Jihwan"https://zbmath.org/authors/?q=ai:do.jihwanSummary: This paper studies an infinite horizon oligopoly model in markets with network effects and segmented demands. In each period, three firms make compatibility decisions before competing in prices for a newly arrived consumer. The firm that made a sale in the last period provides a better product quality in terms of an installed base consumer, which can be shared with its rivals through compatibility. We show that compatibility can be used as an exclusionary device even though it intensifies short-run price competition when firms are sufficiently patient. Under certain conditions, this is the only stable prediction with respect to a dynamic analog of strong stability in network formation games [\textit{B. Dutta} and \textit{S. Mutuswami}, J. Econ. Theory 76, No. 2, 322--344 (1997; Zbl 0893.90043)].Capacity shortages, regulation, and firm incentives in the generic drugs industryhttps://zbmath.org/1530.913292024-04-15T15:10:58.286558Z"Heese, H. Sebastian"https://zbmath.org/authors/?q=ai:sebastian-heese.h|heese.hans-sebastian"Kemahlioglu-Ziya, Eda"https://zbmath.org/authors/?q=ai:kemahlioglu-ziya.edaSummary: Drug shortages are becoming more frequent and severe in the United States, especially for generic drugs. A lack of economic incentives has been cited as a root cause. Only few firms choose to produce a such drugs, and, if they do, these firms do not allocate large levels of capacity. Hence, total industry supply is limited, increasing the odds of shortages. We develop and analyze a stylized game-theoretic model of a generic drug market to understand the impact of various governmental interventions on the total industry equilibrium supply. We explicitly consider firm market entry and exit decisions and the participating firms' incentives to allocate productive capacity to the focal drug market. We first characterize sustainable numbers of active drug manufacturers and their equilibrium capacity allocation decisions for a given regulatory environment. We then analyze the effects of different possible policy interventions on these equilibrium decisions and total industry capacity. Finally, we consider the impact of combinations of different interventions and, importantly, the sequence in which such combined interventions are introduced. A key result of our analysis is that the sequence of policy interventions may have an important effect on the resulting equilibrium industry capacity. When changing the regulatory environment, policymakers should be careful never to lead a sequence of changes with an adjustment that adversely affects pharmaceutical firms' incentives to allocate capacity to the focal drug market; we show that starting with capacity-supporting interventions always is a dominant strategy when aiming to increase total industry capacity.
{\copyright} 2023 The Authors. \textit{Naval Research Logistics} published by Wiley Periodicals LLC.Bilevel optimization and conjectural equilibrium: theoretical results and numerical algorithms (an invited tutorial paper)https://zbmath.org/1530.913302024-04-15T15:10:58.286558Z"Kalashnykova, Nataliya"https://zbmath.org/authors/?q=ai:kalashnykova.nataliya-i"Kalashnikov, Viacheslav"https://zbmath.org/authors/?q=ai:kalashnikov.vyacheslav-v"Flores-Muñiz, José Guadalupe"https://zbmath.org/authors/?q=ai:flores-muniz.jose-guadalupeSummary: We study a mixed oligopoly model, including a nonprivate firm that maximizes the convex combination of domestic social surplus and net profit, under the concepts of consistent conjectural variations (CCVE), Cournot-Nash, and perfect competition equilibria and analyze the behavior of these equilibria. We compare the results to develop an optimality criterion for a parameter, decided by the nonprivate firm, known as socialization level. To work with the CCVE, we need to define the concept of consistency; hence, we also consider a classic oligopoly, which only includes private firms that maximize net profit, and reformulated it as a non-cooperative game, named meta-game, where the players (the private firms) select a conjecture as their strategies; then, we prove that the Nash equilibrium for the meta-game implies the CCVE. After that, due to its similarities with the meta-game, we study the tolls optimization problem (TOP). Taking advantage of the sensitivity analysis for convex quadratic optimization and the filled function method; then, we present an efficient algorithm to solve the TOP. Finally, we apply these results to a financial model in which a group of sectors buy, sell, or exchange a set of instruments; each sector faces some uncertainty when selecting its assets and liabilities to optimize its portfolio structure. The problem is modeled using the concepts of conjectural variations and meta-game and we present results concerning the CCVE.Impact of technology development costs on licensing form in a differentiated Cournot duopolyhttps://zbmath.org/1530.913312024-04-15T15:10:58.286558Z"Kitagawa, Tatsuya"https://zbmath.org/authors/?q=ai:kitagawa.tatsuya"Masuda, Yasushi"https://zbmath.org/authors/?q=ai:masuda.yasushi"Umezawa, Masashi"https://zbmath.org/authors/?q=ai:umezawa.masashiSummary: We investigate how the type of innovation, either of product or process, influences the licensing scheme. For product innovation, we consider a licensing scheme for a patent holder of a new product facing a potential rival who may invest in technology innovation and enter the market for the new product. The alternative forms of licensing schemes considered are fixed fees and royalties. We then compare this licensing scheme for product innovation with that for process innovation studied in the literature.
{{\copyright} 2019 IAET}Technology licensing and collusionhttps://zbmath.org/1530.913382024-04-15T15:10:58.286558Z"Sen, Neelanjan"https://zbmath.org/authors/?q=ai:sen.neelanjan"Minocha, Priyansh"https://zbmath.org/authors/?q=ai:minocha.priyansh"Dutta, Arghya"https://zbmath.org/authors/?q=ai:dutta.arghyaSummary: This paper considers the possibility of technology licensing via fixed-fee, royalty or two-part tariff and tacit collusion between firms that produce homogeneous goods under asymmetric cost structures and compete in quantities. In contrast to [\textit{P. Lin}, ``Fixed-fee licensing of innovations and collusion'', The Journal of Industrial Economics 44, No. 4, 443--449 (1996; \url{https://www.jstor.org/stable/2950525})], all forms of licensing facilitate (obstruct) collusion, if the initial cost difference between the firms is relatively less (more). Technology will always be licensed, and the optimal form of licensing is either fixed-fee or royalty or two-part tariff, but collusion may or may not be possible post-licensing. Welfare decreases after licensing if the firms collude only after licensing but not collude under no-licensing.
{\copyright} 2023 International Association for Economic Theory.Signal-jamming in the frequency domainhttps://zbmath.org/1530.913412024-04-15T15:10:58.286558Z"Taub, B."https://zbmath.org/authors/?q=ai:taub.bartSummary: I examine strategic behavior for a duopoly in a noisy environment. Firms attempt to learn the value of the rival's privately observed demand shocks via a noisy signal of price, and at the same time firms attempt to obfuscate that signal by producing excess output on the publicly observable signals, that is, they signal jam.
In a dynamic setting firms also distort the intertemporal structure of output keyed to the publicly observable demand shock process in order to disguise their private shocks. The net outcome is to radically increase the persistence of elements of output over their full-information value, but also to \textit{reduce} the persistence of price over its full-information value; this latter effect is ``inconspicuousness''.Imperfect collusion in monitored markets with free entryhttps://zbmath.org/1530.913422024-04-15T15:10:58.286558Z"von Auer, Ludwig"https://zbmath.org/authors/?q=ai:von-auer.ludwig"Pham, Tu Anh"https://zbmath.org/authors/?q=ai:pham.tu-anhSummary: Surveys of antitrust cases reveal that colluding firms usually (1) attempt to minimise the risk of prosecution, (2) achieve merely imperfect levels of collusion, (3) compete against some independently acting firms, and (4) adjust to market entries and exits. In contrast, existing oligopoly models neglect some of the four listed stylised facts and, thus, overlook important interdependencies between them. Therefore, the present paper develops a general quantity leadership model that simultaneously accommodates all four stylised facts. The model is a three-stage game in which each firm must make three consecutive decisions: market entry or not, collusion or not, and output quantity. The framework is augmented by an antitrust authority that ensures free market access. In addition, the antitrust authority may directly obstruct collusion and it may threaten prosecution. The results of this study indicate that the latter two instruments are rather ineffective.Constrained-optimal tradewise-stable outcomes in the one-sided assignment game: a solution concept weaker than the corehttps://zbmath.org/1530.913582024-04-15T15:10:58.286558Z"Pérez-Castrillo, David"https://zbmath.org/authors/?q=ai:perez-castrillo.david"Sotomayor, Marilda"https://zbmath.org/authors/?q=ai:sotomayor.marildaSummary: In the one-sided assignment game, any two agents can form a trade; they can decide to form a partnership and agree on how to share the surplus created. Contrary to the two-sided assignment game, stable outcomes often fail to exist in the one-sided assignment game. Hence the core, which coincides with the set of stable payoffs, may be empty. We introduce the idea of tradewise-stable (t-stable) outcomes: they are individually rational outcomes where all trades are stable; that is, no matched agent can form a blocking pair with any other agent, neither matched nor unmatched. We propose the set of constrained-optimal (optimal) t-stable outcomes, the set of the maximal elements of the set of t-stable outcomes, as a natural solution concept for this game. We prove that this set is non-empty, it coincides with the set of stable outcomes when the core is non-empty, and it satisfies similar properties to the set of stable outcomes even when the core is empty. We propose a partnership formation process that starts with the outcome where every player stands alone, goes through steps where the set of active players expands, always forming t-stable outcomes, and ends in an (in any) optimal t-stable outcome. Finally, we also use the new concept to establish conditions under which the core is non-empty.Trade of a common value goodhttps://zbmath.org/1530.913602024-04-15T15:10:58.286558Z"Williams, Steven R."https://zbmath.org/authors/?q=ai:williams.steven-rSummary: When traders have private information about a common value good, adverse selection alone is insufficient to prevent trade of the good and estimation of the common value based upon the traders' private information. We explore sufficient conditions for nonexistence of trading mechanisms in which trade of a common good occurs, along with cases in which such mechanisms exist.Rules versus discretion in central bank communicationhttps://zbmath.org/1530.914052024-04-15T15:10:58.286558Z"Galvão, Raphael"https://zbmath.org/authors/?q=ai:galvao.raphael"Shalders, Felipe"https://zbmath.org/authors/?q=ai:shalders.felipe-lSummary: We propose a theoretical framework to study central bank communication and to assess the benefits of commitment to a disclosure rule. Our model features a coordination environment, where agents have dispersed private information and their interests are not aligned with those of the central bank. Public information can lead to undesirable coordination among agents. We show that anything goes when the central bank cannot commit; both its most and least preferred outcomes can be supported in equilibrium, and so can anything in between. We find that commitment does not necessarily implement the central bank's most preferred outcome. However, the central bank can avoid the least desirable outcomes by choosing an information structure with only two messages that act as action recommendations for agents. Furthermore, our results suggest a higher correlation between fundamentals and outcomes under commitment.
{{\copyright} 2022 International Association for Economic Theory.}Tax authority and taxpayers: how does mutual collecting of information affect the effectiveness of tax controlhttps://zbmath.org/1530.914082024-04-15T15:10:58.286558Z"Kumacheva, Suriya Sh."https://zbmath.org/authors/?q=ai:kumacheva.suriya-sh"Tomilina, Galina A."https://zbmath.org/authors/?q=ai:tomilina.galina-aSummary: Lots of works have been devoted to the modelling of tax control. In the classic game-theoretic formulation, the subject of study is the interaction between tax authority and taxpayers. However, along with such attitude to the problem, some works allow us to study auxiliary problems related to tax collection and tax control. Two of these issues are worth mentioning. The first is the dissemination of information about future tax audits among the taxable population. The second is the gathering and analysis of information on the tendency of taxpayers to evasion. It was shown that both processes can be used to adjust the tax authority's strategy and optimize audits in order to improve tax collection. However, the mutual collecting of information on tax audits by the taxpayers and the tax authority decreases the total tax revenue. The study of formulated problem is accompanied by the modelling of both processes, their simulation, and comparative analysis of the results.
For the entire collection see [Zbl 1522.91009].International environmental agreements under an evolutionary mechanism of imitation and asymmetric countrieshttps://zbmath.org/1530.914582024-04-15T15:10:58.286558Z"Chen, Hsiao-Chi"https://zbmath.org/authors/?q=ai:chen.hsiao-chi"Chow, Yunshyong"https://zbmath.org/authors/?q=ai:chow.yunshyong"Liu, Shi-Miin"https://zbmath.org/authors/?q=ai:liu.shi-miinSummary: Under an often employed imitation mechanism, we investigate whether \(n\) countries with different emission abatement benefits and costs can achieve an international environmental agreement. When the abatement efficiencies, ancillary benefits of abatement, and/or the numbers of countries are large, an international environmental agreement with full participation is the unique long-run equilibrium. For the remaining situations, either no agreement is the unique equilibrium or both equilibria above can emerge with positive probability. These results hold whatever the function forms of countries' abatement costs are, whether the transboundary pollution of emissions is considered, and whether the mutation rates depend on abatement costs and time.
{{\copyright} 2021 International Association for Economic Theory}International environmental agreements under different evolutionary imitation mechanismshttps://zbmath.org/1530.914592024-04-15T15:10:58.286558Z"Chen, Hsiao-Chi"https://zbmath.org/authors/?q=ai:chen.hsiao-chi"Liu, Shi-Miin"https://zbmath.org/authors/?q=ai:liu.shi-miinSummary: This paper explores how the formation and stability of international environmental agreements vary with two often adopted mechanisms: imitating-the-best-average and imitating-the-best-total rules. We first show that the possible long-run equilibria of two dynamics are the same. They are countries' full participation, no-participation, and the two equilibria combined. However, the occurring conditions of these equilibria under two dynamics may differ. Then, we prove that countries' full participation is more likely to be long-run equilibrium in international environmental agreements when imitating-the-best-average rule is adopted. Moreover, all findings of this study hold whatever the function forms of countries' abnoatement benefits and costs are, and are unaffected by the positive affine transformation of countries' total payoffs.
{{\copyright} 2022 International Association for Economic Theory.}Pollution in strategic multilateral exchange: taxing emissions or trading on permit markets?https://zbmath.org/1530.914622024-04-15T15:10:58.286558Z"Julien, Ludovic A."https://zbmath.org/authors/?q=ai:julien.ludovic-a"Kabré, Anicet B."https://zbmath.org/authors/?q=ai:kabre.anicet-b"de Mesnard, Louis"https://zbmath.org/authors/?q=ai:de-mesnard.louisSummary: We introduce polluting emissions in a sequential noncooperative oligopoly model of bilateral exchange. In one sector, a leader and a follower use polluting technologies which create negative externalities on the payoffs of strategic traders who belong to the other sector. By modeling emissions as a negative externality, we show that the leader pollutes more (less) than the follower when strategies are substitutes (complements). Then, we consider the implementation of public policies to control the levels of emissions, namely, two taxation mechanisms and a permit market. We study the effects of these public policies. Moreover, we determine the conditions under which these public policies can implement a Pareto-improving allocation.
{{\copyright} 2022 Board of Trustees of the Bulletin of Economic Research and John Wiley \& Sons Ltd.}Emission reduction of low-carbon supply chain based on uncertain differential gamehttps://zbmath.org/1530.914662024-04-15T15:10:58.286558Z"Yang, Xiangfeng"https://zbmath.org/authors/?q=ai:yang.xiangfeng"Zhang, Peng"https://zbmath.org/authors/?q=ai:zhang.peng.45|zhang.peng.11|zhang.peng.29|zhang.peng.6|zhang.peng.4|zhang.peng.8|zhang.peng.7|zhang.peng.40|zhang.peng|zhang.peng.35|zhang.peng.9|zhang.peng.2|zhang.peng.3Summary: This paper studies the low-carbon production problem based on an uncertain differential game. In a two-stage low-carbon product supply chain consisting of a single supplier and a single manufacturer, we construct an uncertain differential equation by taking the emission reduction efforts of the supplier and manufacturer as decision variables and product emission reduction as a state variable. Based on the uncertain differential game, we obtain the supply chain's dynamic equilibrium strategy, emission reduction, and revenue trajectory under non-cooperative and cooperative situations. By comparison, cooperation leads to more effort on both sides of the supply chain, more carbon emission reduction, and higher profits than non-cooperative ones. To further illustrate the supply chain game in the cooperative situation, we give different income situations under the two distribution methods of Nash bargaining solution and Shapley value, respectively.On the transmission of guilt aversion and the evolution of trusthttps://zbmath.org/1530.914722024-04-15T15:10:58.286558Z"Della Lena, Sebastiano"https://zbmath.org/authors/?q=ai:della-lena.sebastiano"Manzoni, Elena"https://zbmath.org/authors/?q=ai:manzoni.elena"Panebianco, Fabrizio"https://zbmath.org/authors/?q=ai:panebianco.fabrizioSummary: This paper studies the evolution of trust and trustworthiness by modeling the intergenerational transmission of guilt aversion. The results depend both on features of strategic interaction and on parental transmission. We show that if there is complete information of opponents' traits, independent of parenting style, the share of high-guilt agents in society weakly increases over time, and trust and trustworthiness are maximized. Moreover, when traits are not observable, different levels of guilt always coexist, and trust and trustworthiness might also increase when parents have imperfect empathy in the transmission of traits or if there is homophily in society.Optimal control in a multiagent opinion dynamic systemhttps://zbmath.org/1530.914832024-04-15T15:10:58.286558Z"Gao, Jingjing"https://zbmath.org/authors/?q=ai:gao.jingjing"Parilina, Elena"https://zbmath.org/authors/?q=ai:parilina.elena-mThis paper studies optimal control in a multiagent opinion dynamic system. It considers a multiagent system of opinion dynamics with two agents and one player. The opinions of the agents are influenced by the average social opinion. The player influences the opinion of only one agent trying to make it closer to the target opinion as possible. The player can only control the agent at the limited number of periods. The player considers a set of control periods for a given number of such periods and it uses the periods from this set to influence the agent's opinion at these particular moments. The optimization problem is solved based on the Euler-equation approach. Some numerical simulation examples are provided.
For the entire collection see [Zbl 1522.91009].
Reviewer: Yilun Shang (Newcastle upon Tyne)Why direct counter-terrorism measures only may fail: an analysis of direct and preventive counter-terrorism measureshttps://zbmath.org/1530.915012024-04-15T15:10:58.286558Z"Das, Satya P."https://zbmath.org/authors/?q=ai:das.satya-priya"Lahiri, Sajal"https://zbmath.org/authors/?q=ai:lahiri.sajalSummary: We present a two-agent, asymmetric-information game model featuring a terror organization (Org) and a defending state (State). The Org chooses an aggregate terror input. The State chooses the levels of preemptive measures and redress of grievances of the Org's population, respectively as direct and preventive counter-terrorism measures. Defining how the war on terror (WoT) may be ``lost'' or ``won'', we prove that it is impossible to win the WoT with preemptive measures only, if the marginal cost of these measures is increasing. The optimal response of the state to an increase in terrorism is to increase preemption and grant more grievance redress.
{{\copyright} 2019 The International Association for Economic Theory}An extended McKean-Vlasov dynamic programming approach to robust equilibrium controls under ambiguous covariance matrixhttps://zbmath.org/1530.915302024-04-15T15:10:58.286558Z"Lei, Qian"https://zbmath.org/authors/?q=ai:lei.qian"Pun, Chi Seng"https://zbmath.org/authors/?q=ai:pun.chi-sengSummary: This paper studies a general class of time-inconsistent stochastic control problems under ambiguous covariance matrix. The time inconsistency is caused in various ways by a general objective functional and thus the associated control problem does not admit Bellman's principle of optimality. Moreover, we model the state by a McKean-Vlasov dynamics under a set of non-dominated probability measures induced by the ambiguous covariance matrix of the noises. We apply a game-theoretic concept of subgame perfect Nash equilibrium to develop a robust equilibrium control approach, which can yield robust time-consistent decisions. We characterize the robust equilibrium control and equilibrium value function by an extended optimality principle and then we further deduce a system of Bellman-Isaacs equations to determine the equilibrium solution on the Wasserstein space of probability measures. The proposed analytical framework is illustrated with its applications to robust continuous-time mean-variance portfolio selection problems with risk aversion coefficient being constant or state-dependent, under the ambiguity stemming from ambiguous volatilities of multiple assets or ambiguous correlation between two risky assets. The explicit equilibrium portfolio solutions are represented in terms of the probability law.Competitive crowdfunding under asymmetric quality informationhttps://zbmath.org/1530.916022024-04-15T15:10:58.286558Z"Li, He"https://zbmath.org/authors/?q=ai:li.he"Cao, Erbao"https://zbmath.org/authors/?q=ai:cao.erbaoSummary: We proposed a framework on how to design the optimal crowdfunding strategy for the competitive creators under quality information asymmetry. And we also considered the platform uses different funding mechanisms (fixed or flexible) and the creators' different orders of initiation (lead or follow). We find that when high-quality creator initiates first and the degree of quality information asymmetry is low, the optimal price of low-quality creator is negatively correlated with the quality utility and success rate of his own product, but positively correlated with the quality utility and success rate of his competitor's product. More interestingly, we also show that it is more conducive to maximize the profits of creators to retain quality information asymmetry when high-quality creator initiates crowdfunding first. We also find that when the degree of quality information asymmetry between creators and contributors is high, it is always better that the high-quality creator initiates crowdfunding first, whereas it is better for the low-quality creator to initiate first if the of degree of quality information asymmetry between creators and contributors is low. Finally, when the degree of quality information asymmetry between creators and contributors is very high or very low, the two creators and the platform can obtain higher profits by a fixed mechanism; otherwise, the flexible mechanism is more beneficial to them.Risk sharing in public-private partnershipshttps://zbmath.org/1530.916032024-04-15T15:10:58.286558Z"Mukherji, Ronit"https://zbmath.org/authors/?q=ai:mukherji.ronitSummary: Public-private partnerships (PPPs) have been widely used to finance many projects. Despite the growing importance of PPPs, a serious attempt has not been made to come up with a unified theory which can understand the different incentive mechanisms, risks, and heterogeneity embedded in a PPP structure which can often lead to their failure. Using a global games framework, this paper achieves to do exactly that by elaborating upon the role of coordination and uncertainty in these projects. With heterogeneous information, the incidence of failure can be uniquely identified by characterizing and defining the equilibrium. Comparative static results point to how policymakers can improve the probability of success in these partnerships. The incentive mechanisms also highlight how a PPP structure can do better than other forms of investment organization.Short communication: is a sophisticated agent always a wise one?https://zbmath.org/1530.916202024-04-15T15:10:58.286558Z"Zhang, Jianfeng"https://zbmath.org/authors/?q=ai:zhang.jianfeng|zhang.jianfeng.1Summary: For time-inconsistent optimal control problems, a quite popular approach is the equilibrium approach, taken by sophisticated agents. In this short note, we construct a deterministic continuous-time example where the unique equilibrium is dominated by another control. Therefore, in this situation, it may not be wise to take the equilibrium strategy.Evolution of cooperation in a two-species system with a common resource poolhttps://zbmath.org/1530.921502024-04-15T15:10:58.286558Z"Ekobena Fouda, Henri Paul"https://zbmath.org/authors/?q=ai:ekobena-fouda.henri-paul"Martinez de Aguiar, Marcus Aloizio"https://zbmath.org/authors/?q=ai:martinez-de-aguiar.marcus-aloizio"Darcie Marquitti, Flavia Maria"https://zbmath.org/authors/?q=ai:darcie-marquitti.flavia-mariaSummary: Understanding the evolution of cooperation is a major question in evolutionary biology. Here, we extend a previously proposed mathematical model in evolutionary game theory that investigated how resource use by a single species composed of cooperators and defectors may lead to its maintenance or extinction. We include another species in the model, so as to investigate how different intra and interspecific interactions of cooperative or competitive nature among individuals that share the same essential resource may drive the survival and evolution of the species. Several outcomes emerge from the model, depending on the configuration of the payoff matrix, the individual contribution to the resource pool, the competition intensity between species, and the initial conditions of the system dynamics. Observed results include scenarios in which species thrive due to the action of cooperators, but also scenarios in which both species collapse due to lack of cooperation and, consequently, of resources. In particular, a high initial availability of resources may be the determinant factor to the survival of both species. Interestingly, cooperation may be more favored when individuals have less incentive to cooperate with others, and the survival of their populations may depend crucially on their competitive capacities.Age structure, replicator equation, and the prisoner's dilemmahttps://zbmath.org/1530.921532024-04-15T15:10:58.286558Z"John, Sona"https://zbmath.org/authors/?q=ai:john.sona"Müller, Johannes"https://zbmath.org/authors/?q=ai:muller.johannes-c|muller.johannes|muller.johannes.2Summary: We investigate the evolutionary dynamics of an age-structured population subject to weak frequency-dependent selection. It turns out that the weak selection is affected in a non-trivial way by the life-history trait. We disentangle the dynamics, based on the appearance of different time scales. These time scales, which seem to form a universal structure in the interplay of weak selection and life-history traits, allow us to reduce the infinite dimensional model to a one-dimensional modified replicator equation. The modified replicator equation is then used to investigate cooperation (the prisoner's dilemma) by means of adaptive dynamics. We identify conditions under which age structure is able to promote cooperation. At the end we discuss the relevance of our findings.Modelling evolution in structured populations involving multiplayer interactionshttps://zbmath.org/1530.921732024-04-15T15:10:58.286558Z"Broom, Mark"https://zbmath.org/authors/?q=ai:broom.mark"Erovenko, Igor V."https://zbmath.org/authors/?q=ai:erovenko.igor-v"Rychtář, Jan"https://zbmath.org/authors/?q=ai:rychtar.janSummary: We consider models of evolution in structured populations involving multiplayer games. Whilst also discussing other models, we focus on the modelling framework developed by
\textit{M. Broom} and \textit{J. Rychtář} [J. Theor. Biol. 302, 70--80 (2012; Zbl 1325.91013)]
onwards. This includes key progress so far, the main gaps and limitations, the relationship and synergies with other models and a discussion of the direction of future work. In this regard as well as discussing existing work, there is some new research on the applicability and robustness of current models with respect to using them to model real populations. This is an important potential advance, as previously all of the work has been entirely theoretical. In particular, the most complex models will have many parameters, and we concentrate on considering simpler versions with a small number of parameters which still possess the key features which would make them applicable. We find that these models are generally robust, in particular issues that can arise related to small payoff changes at critical values and removal of pivotal vertices would have similar effects on other modelling system including evolutionary graph theory. These often occur where it can be argued that there is a lack of robustness in the real system that the model faithfully picks up, and so is not a problematic feature.Treatment outcome in an \textit{SI} model with evolutionary resistance: a Darwinian model for the evolution of resistancehttps://zbmath.org/1530.922172024-04-15T15:10:58.286558Z"Cushing, J. M."https://zbmath.org/authors/?q=ai:cushing.jim-m"Park, Junpyo"https://zbmath.org/authors/?q=ai:park.junpyo"Farrell, Alex"https://zbmath.org/authors/?q=ai:farrell.alex-p"Chitnis, Nakul"https://zbmath.org/authors/?q=ai:chitnis.nakulSummary: We consider a Darwinian (evolutionary game theoretic) version of a standard susceptible-infectious \textit{SI} model in which the resistance of the disease causing pathogen to a treatment that prevents death to infected individuals is subject to evolutionary adaptation. We determine the existence and stability of all equilibria, both disease-free and endemic, and use the results to determine conditions under which the treatment will succeed or fail. Of particular interest are conditions under which a successful treatment in the absence of resistance adaptation (i.e. one that leads to a stable disease-free equilibrium) will succeed or fail when pathogen resistance is adaptive. These conditions are determined by the relative breadths of treatment effectiveness and infection transmission rate distributions as functions of pathogen resistance.The ideal free distribution with travel costshttps://zbmath.org/1530.923002024-04-15T15:10:58.286558Z"Křivan, Vlastimil"https://zbmath.org/authors/?q=ai:krivan.vlastimil"Cressman, Ross"https://zbmath.org/authors/?q=ai:cressman.rossSummary: This article studies the effect of travel costs on population distribution in a patchy environment. The ideal free distribution with travel costs is defined in the article as the distribution under which it is not profitable for individuals to move, i.e., the movement between patches ceases. It is shown that depending on the travel costs between patches, the ideal free distribution may be unique, there may be infinitely many possible IFDs, or no ideal free distribution exists. In the latter case, animal distribution can converge to an equilibrium of distributional dynamics at which individuals do disperse, but the net movement between patches ceases. Such distributional equilibrium corresponds to balanced dispersal.The partial controllability of linear stochastic control systems with terminal constraints and its applications to game-based control systems with jumpshttps://zbmath.org/1530.930352024-04-15T15:10:58.286558Z"Song, Yuanzhuo"https://zbmath.org/authors/?q=ai:song.yuanzhuoSummary: In this paper, we consider the partial controllability of linear stochastic control systems with terminal constraints. Some necessary and sufficient conditions for this controllability are obtained with the help of backward stochastic differential equations (BSDEs). We establish the equivalence between the controllability of a game-based control system (GBCS), the controllability of a forward backward stochastic differential equation (FBSDE), and the partial controllability of a related stochastic differential equation (SDE) with terminal constraints. By applying our results, we obtain some necessary and sufficient conditions for the controllability of GBCSs with jumps. Then we embed the GBCSs driven only by Brownian motion and deterministic GBCSs into our framework with jumps. Previous results of Zhang and Guo are covered and extended.Multi-event-triggered adaptive critic control with guaranteed cost for discrete-time nonlinear nonzero-sum gameshttps://zbmath.org/1530.932862024-04-15T15:10:58.286558Z"Wang, Ding"https://zbmath.org/authors/?q=ai:wang.ding"Hu, Lingzhi"https://zbmath.org/authors/?q=ai:hu.lingzhi"Qiao, Junfei"https://zbmath.org/authors/?q=ai:qiao.junfeiSummary: In this article, a new event-based adaptive critic algorithm with multiple triggering conditions is investigated to address multi-player nonzero-sum game problems for discrete-time nonlinear dynamics. In order to improve resource utilization while ensure mutual independence among players, the corresponding novel triggering conditions are designed for each player. The corresponding control input is updated only when the relevant triggering condition is violated. It is emphasized that these triggering conditions are established based on the iteration of the time-triggered mechanism. Then, according to the setting triggering conditions, we prove that the real cost function possesses a predetermined upper bound, which realizes the cost guarantee of the controlled system. Additionally, the multi-player closed-loop system is proved to be asymptotically stable and the multi-event-triggered control method is implemented by constructing three kinds of neural networks. Finally, the effectiveness of the developed multi-event-triggered control approach is verified through conducting two simulation examples.
{{\copyright} 2022 John Wiley \& Sons Ltd.}Event-triggered distributed Nash equilibrium seeking over directed graphs and its application to power managementhttps://zbmath.org/1530.932952024-04-15T15:10:58.286558Z"Yu, Rui"https://zbmath.org/authors/?q=ai:yu.rui"Meng, Min"https://zbmath.org/authors/?q=ai:meng.min"Li, Li"https://zbmath.org/authors/?q=ai:li.li.199|li.li.110|li.li.147|li.li.132|li.li.1|li.li.11|li.li.190|li.li.206|li.li.22|li.li.134|li.li.169|li.li.153|li.li.170|li.li.204|li.li.9|li.li.185|li.li.23|li.li.202|li.li.196|li.li.203|li.li.47|li.li.179|li.li.25|li.li.12|li.li.15|li.li.17|li.li.200|li.li.61|li.li.21|li.li.205|li.li.33|li.li.187|li.li.32|li.li.201|li.li.24|li.li|li.li.14|li.li.154|li.li.34|li.li.108|li.li.149|li.li.13Summary: In this paper, the problem of distributed discrete-time Nash equilibrium computation with event-triggered com
munication over directed graphs is studied. Each agent can only receive strategies from its neighbors through a directed and unbalanced graph, while its cost function may rely on the information of all agents. To this end, each agent needs to estimate the strategy profile. Meanwhile, an event-triggered communication mechanism is introduced, which can effectively compensate for network resource loss. Concretely, specific moments that each agent transmits its information are decided by the pre-designed event-triggered condition. In this setting, two discrete-time Nash equilibrium seeking algorithms with event-triggered communication are designed, respectively considering that the Perron-Frobenius eigenvector of the adjacency matrix associated the directed communication graph is known and unknown in advance. It is rigorously proved that both algorithms can linearly converge to the Nash equilibrium with a small error. Finally, a power management example in smart grids is presented to verify the performance of proposed algorithms.Bias cancellation of MixColumnshttps://zbmath.org/1530.940212024-04-15T15:10:58.286558Z"Banik, Subhadeep"https://zbmath.org/authors/?q=ai:banik.subhadeep"Caforio, Andrea"https://zbmath.org/authors/?q=ai:caforio.andrea"Papagiannopoulos, Kostas"https://zbmath.org/authors/?q=ai:papagiannopoulos.kostas"Regazzoni, Francesco"https://zbmath.org/authors/?q=ai:regazzoni.francescoSummary: \textit{S. Carré} et al. [Lect. Notes Comput. Sci. 12244, 3--24 (2021; Zbl 1504.94114)] established a novel bias-cancelling property of the AES MixColumns matrix that effectively corrects any skewed output distribution of a state byte due to a faulty substitution box. Consequently, any effected byte is rendered uniform upon passing through the MixColumns layer.
In this work in progress paper, we revisit and generalize this result and in the process identify a large class of matrices that exhibit this bias cancellation phenomenon and conclude with a foray into how this property is advantageous in the design of countermeasures against Persistent Fault Injections.
For the entire collection see [Zbl 1516.68007].